{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Area under the receiver operating curve\n",
    "\n",
    "Copyright 2019 Allen Downey\n",
    "\n",
    "License: http://creativecommons.org/licenses/by/4.0/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "sns.set_context('talk')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Area under ROC\n",
    "\n",
    "As a way of understanding AUC ROC, let's look at the relationship between AUC and Cohen's effect size.\n",
    "\n",
    "Cohen's effect size, `d`, expresses the difference between two groups as the number of standard deviations between the means.\n",
    "\n",
    "As `d` increases, we expect it to be easier to distinguish between groups, so we expect AUC to increase.\n",
    "\n",
    "I'll start in one dimension and then generalize to multiple dimensions.a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here are the means and standard deviations for two hypothetical groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "mu1 = 0\n",
    "sigma = 1\n",
    "\n",
    "d = 1\n",
    "mu2 = mu1 + d;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "I'll generate two random samples with these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "n = 1000\n",
    "sample1 = np.random.normal(mu1, sigma, n)\n",
    "sample2 = np.random.normal(mu2, sigma, n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we put a threshold at the midpoint between the means, we can compute the fraction of Group 0 that would be above the threshold.\n",
    "\n",
    "I'll call that the false positive rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.301"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thresh = (mu1 + mu2) / 2\n",
    "np.mean(sample1 > thresh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "And here's the fraction of Group 1 that would be below the threshold, which I'll call the false negative rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.325"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(sample2 < thresh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plotting misclassification\n",
    "\n",
    "To see what these overlapping distributions look like, I'll plot a kernel density estimate (KDE)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import gaussian_kde\n",
    "\n",
    "def make_kde(sample):\n",
    "    \"\"\"Kernel density estimate.\n",
    "    \n",
    "    sample: sequence\n",
    "    \n",
    "    returns: Series\n",
    "    \"\"\"\n",
    "    xs = np.linspace(-4, 4, 101)\n",
    "    kde = gaussian_kde(sample)\n",
    "    ys = kde.evaluate(xs)\n",
    "    return pd.Series(ys, index=xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_kde(kde, clipped, color):\n",
    "    \"\"\"Plot a KDE and fill under the clipped part.\n",
    "    \n",
    "    kde: Series\n",
    "    clipped: Series\n",
    "    color: string\n",
    "    \"\"\"\n",
    "    plt.plot(kde.index, kde, color=color)\n",
    "    plt.fill_between(clipped.index, clipped, color=color, alpha=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def plot_misclassification(sample1, sample2, thresh):\n",
    "    \"\"\"Plot KDEs and shade the areas of misclassification.\n",
    "    \n",
    "    sample1: sequence\n",
    "    sample2: sequence\n",
    "    thresh: number\n",
    "    \"\"\"\n",
    "    kde1 = make_kde(sample1)\n",
    "    clipped = kde1[kde1.index>=thresh]\n",
    "    plot_kde(kde1, clipped, 'C0')\n",
    "\n",
    "    kde2 = make_kde(sample2)\n",
    "    clipped = kde2[kde2.index<=thresh]\n",
    "    plot_kde(kde2, clipped, 'C1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here's what it looks like with the threshold at 0.  There are many false positives, shown in blue, and few false negatives, in orange."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_misclassification(sample1, sample2, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "With a higher threshold, we get fewer false positives, at the cost of more false negatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_misclassification(sample1, sample2, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The receiver operating curve\n",
    "\n",
    "The receiver operating curve (ROC) represents this tradeoff.\n",
    "\n",
    "To plot the ROC, we have to compute the false positive rate (which we saw in the figure above), and the true positive rate (not shown in the figure).\n",
    "\n",
    "The following function computes these metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fpr_tpr(sample1, sample2, thresh):\n",
    "    \"\"\"Compute false positive and true positive rates.\n",
    "    \n",
    "    sample1: sequence\n",
    "    sample2: sequence\n",
    "    thresh: number\n",
    "    \n",
    "    returns: tuple of (fpr, tpf)\n",
    "    \"\"\"\n",
    "    fpr = np.mean(sample1>thresh)\n",
    "    tpr = np.mean(sample2>thresh)\n",
    "    return fpr, tpr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "When the threshold is high, the false positive rate is low, but so is the true positive rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.15, 0.501)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpr_tpr(sample1, sample2, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As we decrease the threshold, the true positive rate increases, but so does the false positive rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.483, 0.846)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpr_tpr(sample1, sample2, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The ROC shows this tradeoff over a range of thresholds.\n",
    "\n",
    "I sweep thresholds from high to low so the ROC goes from left to right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import trapz\n",
    "\n",
    "def plot_roc(sample1, sample2, label):\n",
    "    \"\"\"Plot the ROC curve and return the AUC.\n",
    "    \n",
    "    sample1: sequence\n",
    "    sample2: sequence\n",
    "    label: string\n",
    "    \n",
    "    returns: AUC\n",
    "    \"\"\"\n",
    "    threshes = np.linspace(5, -3)\n",
    "    roc = [fpr_tpr(sample1, sample2, thresh)\n",
    "          for thresh in threshes]\n",
    "\n",
    "    fpr, tpr = np.transpose(roc)\n",
    "    plt.plot(fpr, tpr, label=label)\n",
    "    plt.xlabel('False positive rate')\n",
    "    plt.ylabel('True positive rate')\n",
    "    \n",
    "    auc = trapz(tpr, fpr)\n",
    "    return auc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here's the ROC for the samples.\n",
    "\n",
    "With `d=1`, the area under the curve is about 0.75.  That might be a good number to remember."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.761592"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "auc = plot_roc(sample1, sample2, '')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now let's see what that looks like for a range of `d`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZ8AAAEiCAYAAAAmtt8/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzsnXd8FHX6x9/bN703SigJDL0XOyiIBQR7Ows2UE/v53l6yp3ecZ717tRT785yqOApNuyiAhaaKFWKJAyEQICQXjZ1s2Xm98d3UyGYDduSzPv1mtfMfGd25slmdz/zfL/P93l0qqqioaGhoaERSPTBNkBDQ0NDo+ehiY+GhoaGRsDRxEdDQ0NDI+Bo4qOhoaGhEXA08dHQ0NDQCDia+GhoaGhoBBxNfDQ0NDQ0Ao4mPhoaGhoaAUcTHw0NDQ2NgKOJj4aGhoZGwNHER0NDQ0Mj4Gjio6GhoaERcDTx0dDQ0NAIOJr4aGhoaGgEHGOwDQg2kiS5ECJcFWxbNDQ0NLoI0YAiy3KnNaTHiw9CeHRRUVExwTZEQ0NDoytQXV0NJ9lzpokPVEVFRcVs2bIl2HZoaGhodAkmTJhAdXX1SfUWaWM+GhoaGhoBRxMfDQ0NDY2AEzLdbpIkjQE2AwNkWT5ygvMigaeAy4BIYC3wf7Is7wuIoRoaGhoaJ01IeD6SJEnA53RMDN8FrgAeAG4AegPfSZKkBQxoaGhodBGC6vlIkmQE5gFPAs4OnH8GcCFwgSzLX3na1gEHgNsRHpGGhoaGRogTbM/nDOBvwNMIT+aXmAFUA6saG2RZLgHWIERJQ0NDQ6MLEOwxn2xgoCzLxZIkze3A+UOAHFmW3W3ac4CrfG2chkZXQVFUFFXFraooCrhVFbeionrWLdubzm1ag6KqqGon7qse/1qK554t291t7tt0vtKJGwcCVUWnutCrbnSqG73iQqe6Wm23Pab3HNcpbvSqs8UxtzimeF6D0upWiqpQj5NatQG76sSFG5eq4EbBhVusVQUXimfvxO+Z3qUQk19FRFl9u+eYDCZGnDKbQbOv88nb5S1BFR9Zlou8fEkMx89EUI2Ycauh4RWKomJ3ualzuKl3uLE73dQ7xXa9s3nf7lRwKZ4f1RY/oo0/5u62P+wt2lue63KL67jcKi5FwekWx5xupamt8bjTc+6JjrsVFVeI/HjrULDgJIwGwnAQpmvAikPs68TaigOrziGOe9qtjee33dc1oG/zI91R9KgYUNCjYPAsjdt6nXpMW+O2EXdzm+7E76sbcOh0OHTg1OnENp61TkeVQU+Vvs1i0GNrsV/tWdfodag6Xaf+VoNbpXcZDChU6V+kMqBIJbMAzK7W56mA22DFbo3ncJ+zOZp2GoWfO4lP30vCmMGduvfJEGzPx1t0cFzJ10EnP6UaQUdVVRxuhQaXgsOzNDSt3cfsNxxzzrHnNriEYNS1EZSmbc9+g0v72DRiwE0UdUTr6oim1rOuI6rNfrSulmjqPeuWx9t/yg4VnECVXo+thTDYDHpsegM2vQlbm2N1el0rYXG2EBp3J8XCW0yqilEFowqRDSr9i6BPsUqfYuhTopJWCsa2fUEeyqN01ET0wRY3nor4SbhMreOyFJ0eYhMD8FccS1cTHxsw8DjtUZ5jGgFEUVTqnG5q7C5qGpxU2V2ebbGubnA1HatpcFHd4ljjfrVdHAuRh/dWmA16rCY94WYjFpMeg16HQafDoNehb1zrdRh0NLW1197YZtLrMBr0GPU6jAYdRr0ek0GHwbM26vWednGeOKbD1Nje+Fq9DpNB2GRsvJ9eh15H8/0a16obS30h5pp8zDX5mKqPYKzJx1h1BENtIbqGKvQNNnTOOv+9mToDmCPAFOZZwtus27QZrWCygt7U7iUdqptyt50Kdz0V7gYqPNvlbjuVSgOVioMqxUGVuwGbYsfmbqBWcfjvb2yDQWcgyhxFtDmaGEsM0eZosViij9luPC/aEk2kKRJDdR3KgUO4cw/iyM2lIWc/Dbm5uAoK2r9fbCzWYUOxDBlKVa/RHKpP5lBODXW2Y/9mo8WANCmFkVP7kNA70p9vQ7t0NfGRgemSJOlkWW75c5XpOabRCexON7Z6J5V1Ts/aga3e2bQ0tTe2tTgeKNHQ6YQYWIx6zEYDFmPjdsu1odV+uNmA1WQgrHFpuW8+/traeJ5Rj9EQ7HicDuKsB9sRqDwEtsNQebj1uuooqO08Gp8QHVijwRrjWWKbty0t2xvbosAceRwxCQND+yICwvutc9VRbi+nwl5Bhb1CbDdUUGmvbNpuPFbRUEGts7Zz71cLrAZr049+jCWGGHNMs1BYogk3hmM2mDHpTZgNZrHozZgMplbrVu0GMxaDhXBjOLoOeEeK3U79zp3Ub11N3dZtFGVn4y4rO+FrTH37Yh0iYZGGYB02FOvQoRhTU1FV2PhJLttW5AHlTefHJIchTU4lfVgCYVEmwmPMGE2Gk337ToquJj4rgT8C0/FEvEmSlAScBTweRLtCmgaXmwOltewrqiGnWCz7S2oorxUi4suuJ4NeR5TVSKRFLE3bVhNRViNRlsb9lsdNhJmFeDQKR1sxMep1Hfoid0sUBWoKoTxXLGX7oeJgs9jUlnT8WhFJENMXYvuKdUyf1qLScjFHgt43AlzrrKWwtpDC2kKK6oqatlvu17k673kZdAZiLbHEWePEYokj1hIrBMUjJi3XjdtWo9Unf583uG026rZto37rVuq2bqP+55/BefyZJsa0NCwZGVgyBmLOyMCSmYll8GAMkcd6K/YaJytf/ZnD2RUAJKVHMXhSCv1HJhKbEu7Xv6kzhLT4eIQlA8iSZblKluW1kiStBt6RJOn3CGlfCFQCLwbN0BDB7nSzr6iGvUXV5JTUsK9IiExeWa1XHkqE2UBMmImYcDMxYUZiw8zEhJmIDTcR7Vk3tkVZjZ5FbFuM+p4rEieDokD10WZxaRSa8gNi7erAeIrOANG9m4Wl1TodYnoLL8THqKpKcV0xB6sOUlBb0CwsdYUU1RZRVFtEtbPaq2taDVbirEJA4q3xrUSlcTveGt90PMochV4Xmp6qs6iIui1bhNhs2UrDvn0cL7TQnJlB+PgJhI0ejWVQJuYBAzFERnToHiWHqvnypV1Ul9sBGD29L6dekoEhhL33kBYfYCbwOnA2sNrTdinwDPAPxDyl9cCVsixXBMPAYKCqKgU2O9kFVewprG5a55bUnFBkoixGMpIjGZQcSUZyJCnRFiEyLcXFasJsDN0PbJdGcUNV/nHEZb9Yuxt++RrRfSB+gFhi04WoNIpMVBoY/PeVVlWVkvoScipz2F+5v9XSUXEx6owkhSeRGpFKangqqRGppESkkBqeSnJ4MvFh8cRZ4gg3hd6TekdQVRXHgYPUbd1C/Zat1G3divPIcbKFGY1Yhw0jfPx4wieMJ2zcOIxxcR2+R01FA4X7bRTst1GYa6P0SA2qomI06znn+qEMmpji47/M9+jUzgT3dyMkSaoM9ZIKB0tr+TG3jOyCKrILq9lTUEWV3dXu+fERZjKTI8n0CI1YR5ESbdG8kkBQUwJFuzwi0yguuaKrzP1LA946ISTxAyB+ICRkiHX8QIjr7xfPpS2qqlJaX9osMjYhMDmVOVQ72hcZvU5PYlhiK2FJjUglJTylaTvBmoBBH9yxBl/irqrCnr0He1YW9du2Ubdt23HHa3RhYYSNGU34OI/YjB6NPrzjAutyusnbVUbOtmIKcmzUVh77oBKdFMYF80eS2Mf/AQSekgo2WZZjO3uNUPd8ejSqqrJo3QGe/GoP7uO4NCaDjszkKIamRTE0NZohaVEMSY0mKcoSBGt7IIoCFQegcCcU7ITCXWKpKTzx63R6j8C0EZdGgTEG5v+nqipl9rImkcmpzCG3MpecyhyqHO2XatHr9KRHpZMRm0FGbAaZsZlkxGbQP7o/ZoM5ILYHGlVVcRWXYM/OoiE7G3tWNvbs7ON7NYjIs7Dx45s8G+vQoehMJw66OOaeisrRfZXs3VRIzrYSHPWtHziNFgMp/aNJy4ghNSOG3oNiMZq7jrBr4hOi2Oqd3P/+DlZmiXm4CRFmRvSOYWhaNEM9IjMwKQJTCPfpdiucdijOahaYwp1QtBscNcc/X2cQ3WJtxSU+Q7QbA/sj7XA7yKnMQS6X2VuxF7lCrG0N7c9Q0Ov09I3qS0ZMG5GJ6Y/F0H0fcFRFwZGXJ0Qmew/2bCE0J4pAM/VLJ2zU6CaxMQ8ciK6TwRpl+TXs3VTI3k1F1FQ0ezg6vY6+Q+PoPzKR1IExJPSOQN+Fv/+a+IQgP+fbuPOtbRwqF9E/l4/vw1/njCCsCz3VdGnqyoW4NAnNLiiR2w9XNkVA6ghIHQWpI8WSPEzMUwkCpfWl7C0XAiNXyMjlMgdsB3C3Y78OnRCZFgKTGZvZ7UWmEdXppGb9emrXf489O5uGPXtQ6tqJvDOZsGRmYh0qwputw4ZikYZ0ODDguPdXVEqP1HAoq4x9m4spy2/9QJPcPxppcgqZ41MIj+4+nqUmPiGEoqi8s/kwCz/bjcOlYDHq+eucEVw5sW+wTeueOGqhdC8U74ESz1L4M1S1W04KIlNai0zaaIgb4LOQZG9wKS4O2g42icze8r3sKd9Dmb39J/R4azxSnIQULzE4bjCZsZkMiBkQlJDjYKKqKvasLGyffELV58txl5cfc44+PBzLkCFNImMdOhRLZiY688kLQFVZPUeyKzi8p5wjeyqw17QOtY5OCkOalMLgSakhGSbtCzTxCQFcboXluwr4z3f7kYvEgG6/hHD+86txDO+llSk6aRpqoFRuITIylGSLeTLtooOEzBYiMwpSRkJUcKKIqh3V7CnfI7rMymX2lO9hf+V+HO3M2DfoDPSP7s/g+MFNYjMkfgiJYcFJpRIqOAsLsX32GbZPPsGRs7/5gE5H+IQJhI0Z0yQ0pvT0TnedtcVe6yR/b4UQnOxybCXHhs5HxVvpPzKBwZNTSRkQ3e2DgzTxCSIOl8KH247w4pr95JU1u/mzRqXx+KUjibZ6N0DZ47FXCU+mZA8UZ3tERgbbiUQGCIuH5KGQJEHKcOHZJA8DS3DSjrgVN7m2XHaW7GRHyQ52luwk15aL2k4m4yhTVJPIDIkfwuB44dH0hC6zjqDU1lL99dfYPvmE2h9+bDXHxpyRQczFc4i56CJMqak+va/D7kL+sRB5YyHFB6uOmdpjCTfSW4qj79B4+gyJIyYprNsLTks08QkC9Q4372w+xCtrcymwiUlhOh1cMCKVO6dmMqK35u2cEFUVKWOaosw8618SmYgkSBoiRCZpSPMSmRQYu9uhwl7BrtJdbC/ezs7Snfxc+nO7qWP6RvUVAhPX7NGkRaT1qB+tjqC63dRt2oTt40+oWrUKtcUYjiEujuhZs4iZMwfr8GE+f+8qi+rYtfoIe34owGFvHmfTG3SkZcTQZ2g8fYfEk9QvCr2+5/7fNPEJMPuKqrnu1Y0UVYkoFoNex5wxvbhzagaZyVFBti4EURQxR6ZwRwuh2QF1J8h9FZniEZihrYUmIiFwdreDU3Gyt2IvO0t2Ni2Hqo8vmvHWeEYljWJ00mhGJ41mWMIwIkydH9juCTiO5FP57rvYPvsMV2FzyLvOZCLynHOImTOHyDPP8Drs+ZdQFZVDWeXs/O4Ih3Y3fzYNJj2DJ6WQMS6ZXpmxmCxa0FAjmvgEkJoGF/Pf3EpRVQNmg54rJvTh9ikZ9I3vngOKXuNyeAb9PZ5MwQ4o+rn9cGa9CVKGiW6ytNGQMkKITXh8YO0+AcV1xU0is6NkB1llWdjd9mPOM+qMDIkf0iQ2o5JG0Tuyt+bRdBBXeTmlL71ExdvvtMqTFjZ2LDFz5hB9wfkYYnzfo9BQ72LPhgJ2rTmCrbh5HCcq3sqIKb0ZdnovrJFa9/nx0MQnQKiqygMf7CS3pBaTQce7809hbHrH0ml0SxpqxDyZgh3NXk3JnvYzAJgjPYP/o8Tgf+oo4c0EeL7ML1HjqOGbQ9+wLn8dO0t2UlB7/BT4KeEprbyaIfFDelzEmS9Q6uooX7KEskWvotSKrkpjSgqxl11KzOzZmPv398t9q8vt/LQij+wfC3E1NHet9ZbiGHV2H/qPSuzRXWodQROfALF4w0GW7xQ/RH+aNaxnCk/VUdj8KmR/CqX7OH5dQCA8sVlg0kZB6mgxQTMI4cwdweF2sC5/HV/kfsGaI2toaJOjzaw3MzxxOKMSRzEqSSypEb4d3O5pqE4nlR98QMm//427pBQAfUwMifPmEfera9Fb/SPk9dUOtn6Vx89r8nF7ssEbzXqkU9IYObU3Cb2CE6TSFdHEJwBszavgseXZAMwZ04vrTukXZIsCiKrC4Y2w8SXI+vTYiZox6a2FJm20SJAZ4t1NiqqwtWgry3OXsypvVat0NBaDhTN7n8mE1AmMThqNFCdh+oV6NhodQ1VVqlespOTZZ3Hk5QGgs1iIv+F6Em691S9dayC617avOsSObw7j9Hg64dFmxs5IZ+hpaVjCtf+vt2ji42ccLoXfvP0TLkVlUHIkT1w6smf04zvtsPtDIToFO5rbI5Jg3I0w4CzRjRZC4zO/hKqq7K3Yy/Lc5Xxx4AuK6oqajul1eianTmbmwJlMS59GpFl7AvY1tRs3Ufz009h37hQNej0xl15C0l13+TxMuhGnw82u746wbUUeDXUit5ol3Mi48/ox8uw+mLSsI51GEx8/8/FP+eRX1mPQ6/jPr8YRbu7mb3lj19rW11tHpKWNgVPugOGXBCxxpq/Ir8nni9wvWJ67nP22/a2OjUgYwcyBMzmv/3kkhQc3ZLu7Yt+zh+JnnqF27bqmtshp00j+7T1YMjP9ck+3SyFr/VG2fHGQuioxDmm0GBgzrS9jpvfVPB0f0M1/CYOLW1F5aa34sZo9uheDUrppKHXLrrXsz0DxZN/VG2HYxTB5PvSZGPJdaS2psFew4uAKlucuZ3vJ9lbH0qPSmTlwJhcOuJD+Mf2DY2APwHEkn9IXnsf26WdNE0PDxo4l+f77CB83zi/3VNwK8sYitnxxgKpSEZVoMOoZMaU3487r161yqwUbTXz8yMrdheSWiAic26dkBNkaP3CirrXxN8GEmyE6LXj2eYGqquTactlYsJH1+ev54egPuNTmFPYJ1gQuGHABMwfOZHjC8J7RdRokXBUVlL30MhVLl6J6wqbNGRkk/+5eIs8+2y/vvdutsHdjIVu+zKPKk/pGp9cx9LQ0JlzYn6h4LRLR12ji4ydUVeXFNcLrmT40GSm1G3k9VQWweRFsXQx1pc3tXahrTVVVjtQcYVPBJjYWbmRTwaZjEnJGmCKYlj6NmQNnMil1Eka99nXxJ46DB6n8+GMq3nwLpUbM7TKmpJD0m7uJmTMHndH377/brSD/WMjWLw82eTo6HWROSGHSrAHdNqlnKKB9m/zE9zll7DwiaqXcMdU//dIBpzQHNjwHO95pno/ThbrWimqL2FS4SSwFmzhae/SYcxLDEpmYOpFp6dOY0meKNvfGz7grK6n68ktsH39C/Y5m71kfHU3ivNuIu+46v4RNtyc6gyamMOHC/sSlapkk/I0mPn7ixTU5AEwaEM/4fl18Ts/R7bD+Wcj6hKa5OeGJolsthLvWyu3lbC7czKYCITgHqw4ec060OZpJqZOYlDaJyamTGRAzQOtS8zOqw0HN2rXYPvmE6tVrWmUkMKalEXPxHBJuvBFDbKcrNLeL2yVEZ8uXB6kuaxadwZNSGX9BP010AogmPn7g53wb3+eILpw7p3bRsR5VhYPrYf0zsP/b5vbYdDjtNzD2OjCFBc++41DjqGFL0RY2FmxkU+Em9lbsPeaccGM441PGMzltMpNSJyHFS+h1oTl5tTuhqir2nTtF/ZzlX+C2NVdQ1YeHE3X++cTMmUP4xAk+K2PQErdLYc8PBWz9Mo/q8haiMzmVCRf017rXgoAmPn5g2VZRjGxwSiRTBnex8FtFgb1fwrpnIH9Lc3vyMDjjtzD8UjCE1sem0l7J4t2LWbpnKfWu1nVSzHozY5PHMiltEpNSJzE8cTgmvRYmGygcR/Kp+uxTbJ98iuPgweYDej0Rp59OzOzZRE2fhj7MPw8ybpdC9oYCtn51kJpykXlCp9chTUphvCY6QSW0fkW6AW5FZfkukUbn4rFdKDGk2wm7lsH3/xQ51hrpOxnOuBcGzQi59Da2BhtLdi/hrey3qHOJlPlGnZGRSSOZlDqJyWmTGZU0SqtrE2Dc1dVUr1iB7eNPqNuypdUxiySJRJ+zZmJKTvabDQ31opbOT6vyWovOZI/oJGuiE2w08fExP+aWUVItPuwXjeoVZGs6gKLAtsXC07Edbm4fNEN4Ov1OC5pp7VHtqObNrDd5I+sNapwiKirKFMUNw2/g2qHXEm2ODrKFPZO6bduoePMtqr/5BrWhOb+dISmRmFkXETNnNtYhQ/x2f1VVKc6rZve6fPZtLsLlELnXdHod0impTLigHzFJmuiECpr4+JhPt4sIqnHpsaFfKqFsP3xyFxzaIPZ1etGtdsY9IvVNiFHrrOWt7LdYvHsx1Q5RbjzCFMH1w67n+mHXa6ITBFRVpe6HHyh98SXqNm9uatdZrURNn07MnDlEnHqKX8KkG3HUu9i7uYjd6/IpPdxcfsNo1jN4UirjzutHTFJojU9qeCk+kiSZgfnALCAduBmoB64B/iHLconPLexCNLjcfPmz6HKbPTqEvR5FERNDv3kEGsdIRl8LU+4X2aNDjDpnHW/veZvXd7+OrUEMVIcZw7hu6HXcOPxGYixa5ddAo6oqNatXU/rSS9h37Gxqt44cSdzVVxN13gwMkf7Nb1ecV8Xutfns3VLcqqxBQu9Ihp/Zi8GTU7GEac/XoUqH/zOSJEUB3wATgEIgBQgD0oD7gSskSTpLluUj/jC0K7BubylVdhd6HcwM1S630hz45Ndw+EexH90HZj8PmdOCa9dxqHfV8578Hq/9/Brl9nJAiM7VQ65m7vC5xFu7TlLS7oLqdlO9ahWlL71Mw57mscHwiRNJuH0+Eaed5tdxTofdxd5NRWStP0rJoeqmdqNJT+bEFIaf0YuUAdFdZ6y1B+PNY8FfgVHADGA7UAwgy/KHkiTNAZYCjyC8oR7Jhv0ivHpC/3iSokJskFtxw48vwrd/BZenkub4uXDuX8EaWt1VdpedZXuXsWjXoqasAxaDhaukq7hpxE0khiUG2cKeh+pyUbV8OaUvv4IjN7epPeKMM0i8fT7hEyb49f7FeVXsXn+UfZuKmkoaAMT3imD4mb2RJqdoyT67GN6Iz+XAf2RZ/lqSpISWB2RZ/kySpH8D13prgCRJ1wAPAQOBg8ATsiy/cYLzk4C/AecBVmAD8FtZlvd5e29fsyu/EoCx6b6fHHdSlO7zeDsbxX5MX+HtZJwTXLva4HA7WLZ3Ga/uepXi+mJAhEpfIV3BLSNu0bJGBwHF4cD28ceU/XcRzsPNASmR06aRePt8wkb6b2zQYXexb3MRu9e19nIMJj2Dxicz/KzempfThfFGfBKB7BMcPwB49esgSdIVwFvAc8BXwMXAEkmS6mRZXnac83XAR0Am8HugDPgL8J0kSSNlWa7w5v6+xK2o/JwvCoqN6h0i4qO44cf/wLePtvB2boJzHwkpb0dVVT7P/Zzntj3XVCPHqDdy2aDLuHXkrVrVzyCg2O1Uvr+MsldfxVVYKBp1OqIvuICE+fOxSoP9du+SQyJibe9xvZxeDJ6UijVC83K6Ot6IzwFgIvDfdo6fi/BcvOEJ4D1Zln/r2V8hSVI8oovvGPEBBgGnAzc2ekeSJGUD+4HZwBIv7+8z9pfUUO8UX5RRfUJgALxkL3xyJxzxRCDFpHu8nbODa1cbbA02HvnhEVbmrQTEPJ2LB13MvJHzSIsMzbQ93Rl3VRUV775L+eIluMs8iVYNBmJmzybhttuwDBzgl/s6HW72bRIRa8V5rb2czPHJDD+zN6kDNS+nO+GN+CwCnpQkaRPwpadNlSQpGvgjcAmi+6xDSJI0EMgAFrQ5tAy4UpKkAbIsH2hzrDHDYHWLtnLPOoEg0phENCbMRJ+4IIZ1Km744d/C23F75lpMuFl4O5bQyqy9uXAzf1j/BwprxZP1tPRp3DfhPvpE9QmyZT0PZ0EB5UveoPL991FqRRkQnclEzOWXkXDLrZj79PbLfVVV5cCOUta9u5eaiua5QXFpwsuRJmteTnfFG/F5BhgBvAIonraPgChAB3yCGIvpKI2zzeQ27TmetYTwtpqQZXmnJEnfAX/yeDxlwNNADfCxF/f2ObuOiPGeUX1igvd05rTD21dD7ndiPyYd5rwAA6cGx552cCpOXtz+Iot2LUJFJcwYxoOTHuSSzEu0J9sAY5dlyl97DdvyL8Al6hfpw8OJveIK4m++GVOK/7IQ2ErqWffeXvJ2CQ9Lb9QxaHwKw87sRVpGEL9HGgGhw+Ijy7IK3CRJ0hLgMkSAgAHR1fapLMtfeHnvxr6pqjbtjV5Ne4MSdwAraB5/agAulmU5t53zA8LOfOH5jOwdpC43txPev7FZeCbcAuf+JeS8nUNVh3hw3YPsKt0FwLCEYTx15lNaRdAAoqoqdRs3UrboVWrXr29qNyQlEn/9DcRddSWGGP99jt1OhZ9W5bHlyzzcTvEcmz48nrOuHqxlIOhBeDPP5ywgW5bl1cDq4xzvC5wly/JbHbxk42ON2k670qYdSZKGIqLbcoB7gDrgNuADSZLOl2V5XdvXBAJFUckuEBoaFPFR3PDRfNj7ldg/7wk49c7A23ECVFXl0/2f8vjGx6lz1aFDx9wRc7l7zN2YDFq3SiBQXS6qVqyg/NXXsGdlNbWbBw4k4eabiJ49G73Zv2WiD2eXs/advVQWiVx8EbEWzrxyEAPHJmmeTg/Dm26374DrgLfbOX4e8Dwieq0jNOZUb+vhRLU53pLGwIQZjZFtkiStAtYBzyImwAac0toG7J4nuAFJAa4Hoqrw+T3w8wdi/+w/hpzwVDmq+OsPf+Wrg0Ick8OSefzMx5mcNjnIlvUMlLo6Kj/4kPLFi3Hm5ze1h40fT8IttxA5dYpfyhi0pNbWwPfv72PfFhFCr9Prst+jAAAgAElEQVTrGH1OHybOGoDZqmUh6Im0+1+XJGkA8HCLJh0wX5Kkc49zuh6YCngT6tw41pMJ7GrRntnmeEv6AVktQ6plWVYlSVoP/J8X9/YpBZX2pu1esQEMNlBVWPFH2OaZFnXa3XDW/YG7fwfYWrSVBesWUFAr0g5NS5/GwlMXEmsNkXD0boyrtJTyt96icunbzfVzdDqipk8n4ZabCRszxu82KG6FXWvy2fhpLk67iAZNy4hhyrUSCb39m35HI7RpV3xkWT4gSVJvRAg1iO6xszxLWxSgBDH3pkPIspwjSdIBxOTVj1ocugzYJ8vyoeO9DLhRkqS4NnN6TsH7MG+fcbRS5EeLshiJtgawC2nNU/Djv8V2Y7aCEOm6cCkuXtrxEv/d9V8UVcFqsPL7Sb/n8kGXa90rfqbhwAHKX1+M7eOPUR2i3LnObCbm0ktImDsXc//+AbGj8ICNNUvlpmSf1kgTp12ayZBTUtHptc9AT+eE/q4sy+c1bkuSpADXybK81If3fwR4XZKkCuBzxFydK4GrPfdMQoRjZ8myXIWIuLsOMR/oScSYzw3AlMbXBIN8j/gE1OvZ8C9Y/YTYHnE5zHwmZITncPVhHlz3IDtLRMLJofFDefKsJxkYE3pJS7sTdT/9RPlrr1H99TfCKwYMMTHE/epa4n71K4wJgZmNYK918sPH+8laf7RpRHfYmb04dU4G1khtfE9D4E1n6wCEd+MzZFleLEmSBbgPuBXIBW6QZfldzykzgdeBs4HVsiwflCTpdOApYDHC49oFnCvL8te+tM0bCmyi2y0t1voLZ/qIrYth5R/F9uAL4JKXQG8IzL1/gc/2f8ZjGx+j1inmiswdPpe7x96N2eDfgeyeTMO+fRT9/e/Urm2OtzH17k38TTcRe+kl6MMDE0GmKip7fixgw4f7sdc4AUjsG8mUayRSB4bAxGuNkMKbUOs8AEmSxgCRiHGelteJAs6RZdmrsRdZll8GXm7n2GKEyLRsy0Z4SCHD0UB6PruWwWf3iO0BZ8EViyEEosUKawv52+a/sSpvFQBJYUk8esajnNYr9IrRdRdcZWWUvPACle+9L8pkANbhw0m45WaiZszwaw2dlqiqyuGscjZ9foCiAyLq02Q1MHn2QEZO6Y3eEFoVcDVCA29CrYchJnJmnOA0hSAO/AeLRvHp7W/x2fe1CKlGhT4T4eq3wRQgb6sdnIqTt7Le4j87/kO9pzbQ1L5TeeS0R4izxgXVtu6KYrdTvuQNyl55pSkbgblfP5Lvv4/IadMCNqamqiqHdpezeXmz6AAMmpDM6ZcPIiI2xDK7a4QU3jwaPYkoIPcUQmT+APwaiAPmAr0B/4fPhCBHPd1uvfzZ7XZkC7x3PSguSBkBv3ofLMGNFtpcuJnHNz5OTqVIShFvjee+Cfcxa+AsLajAD6iKQtXyLyh+9hlcR0X0oCEmhsRf/5q4q69C5+c5Ok12qCp5P5ex+fMDrfKw9ZZimTRrAL0GaQ8dGr+MN+JzOvCKLMt/kCQpDHgAyJFleZWnnMJ24HfA7X6wM2RpcLkpqRY5qXrF+MnzKZHhrcvBWQex/eC6DyAseF/w0vpSnt7yNJ/nfg6AXqfnaulqfj3211opaz9Rt3UrRU8+hX2XZ1aCyUT8ddeRePt8v2YjaImqqhzcVcaW5a1Fp8+QOCbOHECvQVr4vEbH8UZ8IhECgyzL9Z4w6XHAKlmWbZIkvQrc6AcbQ5pCm5/n+Njy4X+XQn0FhCfC9R9BVHBKDLgUF+/K7/Kvn/5FjVOEz45KGsVDkx9iaMLQoNjU3XHk5VH8j6epXrWqqS3qvPNI/t29mNPTA2JDY/LPLV8cbFVXp+9QITppmZroaHiPN+JTTOvM0TlAy0pSBUCI1o72H41eD0BytI/7uOvK4c1LoeoImCPhumWQcKIhN/+xvXg7j218jD3lonRyrCWW347/LRdnXoxepw0o+xp3ZSWlL75E+dKl4BSRY9ZRo0h58AHCx40LiA2qIkRn8xcHmubqAKQPi2firAFaBJvGSeGN+HyLyHDwsadq6DbgVkmS4mVZLkeU1y71h5GhTJXd88Ng0mMx+jDc2VEnMlSX7AG9Ca5+C3qN9d31O0iFvYJntz7LRzliHrAOHZcNvoz/G/t/WpYCP6A6HFS8/TYl/3kRxZOVwNSrF0n33kv0hRf4PQ0OCNHJ3V7C5uUHKctvITrDE5g4s78mOho+wRvxeQTYCOyRJCkFeBER2SZLklSMKJHwD9+bGNrY6oX4xIT5MNzZ7YT353rKXuvg0lcCXhZBURWW7V3Gc9ueo8ohIpmGxg/l4VMeZmSS/0on91RUVaX6668p/sc/cOaJ5B76iAgSbp9P/A03oLf4P3JMVVRythWz5YuDlB+tbWrvNzKBiRcOIGWANp6n4Tu8meez3xNuPVeW5VIASZKmAn8H4hG1fBb6wcaQxlbnY/FRVfj0N7Bvhdi/8O8w4lLfXLuD5NpyeXj9w+wsFRkKosxR/Gbsb7hi8BUYQmQya3eiftfPFD31JPVbtooGg4HYK68g6a67ApaVIG93GRs+yGklOv1HJTJxZn+S+2mio+F7vJnn8yfga1mWmwrGybK8FTjHH4Z1FarsogCXz3K6fb0QdngyGJ31e5h0m2+u2wFUVeVd+V2e3vI0drcIpJidMZt7x99LQlhQC8V2S5xHj1L87D+p+uyzprbIKVNI/v39WDICM7bnsLvY8EEOu9cdbWobMDqRiTMHkJQeWrWgNLoX3nS7PQDUIurpaHjwabfboY3w/T/F9vi5cPYfTv6aHaS0vpSHv3+Y9fmiuFiviF48esajTEydGDAbegrOoiLKFr1K5XvvoTaIgBWLJJHywO+JOC1wGSEKc22sej2LqhIxOTgtM4YzrxpMUl9NdDT8jzfiU0Rz9VEND43iE32y4qMo8KUnKXjamIAmCv320Lcs3LCQigaRKPyigRexYPICoszaj5AvcR49StmiRVS+vwzVE8FmTEoi6Z7/I+bii9EZAtOl6XYpbP78ANtW5KGqonz15NkDGTM9Hb2WbVojQHgjPvcBr3nKLKxEhF67254ky/JaH9nWJajyleez/U0o2C62L/hbQBKF1jnr+Nvmv/HBPlGILtoczcOnPsz5/c/3+717Eo4jRyh7+RUqP/64KWzakJhIws03E3f1VQFL/AlQdrSGr1/PagqdTugdyfSbhpHYR6utoxFYvBGfZZ71TYh0Om3RIRKo96gRaZ94PvWV8PVfxPaoqyDd/xU+d5TsYMG6BRyuPgzA5LTJPHr6o6RGBGcCa3fEkZdH6cuvYPvkE3CL5zRjcjIJt95C7BVXoA8LXAkOVVHZ8e1hfvw4F7dLAR2Mm5HOpFkDMZi0eVoagccb8bnJb1Z0YZrE52RKAa/5G9SVgikCpv/FR5YdH5fi4pWdr/DKzldwq25MehP3jLuH64Zdp00W9RENuQcoe/klbJ993pRt2piaSsK824i97LKAhE23pKqsnm+XZJO/txKA6EQr0+YOo5eWmUAjiHgTar3En4Z0Vao90W6d7nYrkWGTp6LElPshOs1Hlh3LoapDLFi3oCmEelDcIJ4880kGxw322z17Eg379lH60stUffFFUzE3U69eJMyfT8wlF6MPUOLPRlRVRf6xkHXv7sXhKWE97IxenH55JuaTeVjS0PAB2ifwJDmpaDdVha8eFJmq4wfCKXf62LpmNuRv4J7V9zSVPbhx2I3cPe5uLAYt7f3JYpdlSl98ieoVK5pFp29fEm+fT8zs2ehMga+3VF/tYPVbMrnbRf3HsGgz51w3hP6jEgNui4bG8dDE5yRwuRVqGjzzfDojPvIXsP9bsX3eE2D0jxDkVORw75p7qXfVkxyezONnPM7kNP+PK3V36nfvpvTFF6n5+pumNnO/fiTccTsxs2YFrJhbWw7uLOXbN/dQX+UAYOCYJKb+SiIsSqsmqxE6aOJzEjR2uUEnPB+nHb5aILYzp8Pg83xoWTMV9gru+vYuap21JIcls/TCpaREpPjlXj2F+p07Kf3Pi9SsXt3UZs7IIPH220X+tQCFTLfFYXfx/fv7yPpe1PoxWw2cefVgpMmpWn0ljZBDE5+ToNHrAYi0ePlW/vAvqMwDvRHOf9Ivc3qcbif3fHcP+TX5WA1Wnp/2vCY8J0HdTz9R+p8XqV23rqnNMmgQiXfeIcpWB0l0AI7mVPLN4iyqSkVmit6DYznnxqFEJwQuok5Dwxs08TkJHG6ladti9CJSzJYP654W25Nvh8RBPrZMDDY/8uMjbCveBsBjZzzG8IThPr9PT8BVXk7RE0+2SoNjGTqUxDtuJ2r69IBkmm4Pt1Nh0+e5bFt5CFQwGPWccvFARp/TF502YVQjhPFafCRJugiYhSip/QdEyp1pwOuyLNtP9NruhsPVLD5mb8RnzZOiKmlEMkx5wA+WwZLdS/g452MA7hpzFzP6z/DLfbozqqpS9emnFD3xJO5KEaZsHT6cxF//msizpwa9K6ssv4ZVr2U1lT1I7CsmjCb00iaMaoQ+3iQWNSEmms4CFECPyGg9CPg3cJMkSefJslzhD0NDkU6Jj+KGbM8T9Jn3gtX3GYNXH17NM1ufAeDCARcyb9Q8n9+ju+M4fJjCPy+kdoNIZaiPiiL5/vuIvfzyoHo6IERx99p81i/Lwe1U0Olg3Pn9mDhzAAZvHoI0NIKIN57PQ8BMYD7wFXDI0/4hoq7P08CfgN/60sBQpmW3m8nQwS/9kS2iJDaAdKHPbZLLZR5Y+wAqKqMSR/HI6Y8E/Qm9K6G6XJQveYOSF15AtQtHPuq880j54x8wJScH2Tqw1zj59n/ZHNgh6jZGJ1qZftNw0jK0tIsaXQtvxOc64DVZlhdJktSUX1+WZRfwgiRJEjCHniQ+Hs9HpwNjR/vX960U66QhENfPp/aU1pdy97d3U+eqIzUilefOeU6bx+MF9qwsCh56GHtWFgDGlBRS//QwUdOmBdkyQf7eCla9lkVtpciEPWhiClOulbCEaUO3Gl0Pbz61fYAtJzi+E7jl5MzpWjSKj9mg77h30Sg+g871qS0N7gbu+e4eCmoLCDOG8a9z/kVimDahsCMo9fWU/vvflL2+uCkHW9y115B0770YIoM/fqK4FTYvP8iWLw+CCkaLgSlXD0Y6RQuh1ui6eCM++YhS2e0xCSg4OXO6Fg2N4tPRfvaqAigUqW0Y5Lt5PaqqsnDDQnaU7ECHjqfOfAopXvLZ9bsztRs2UPDnhTgPiwSr5owM0v76COHjxgXZMkFVaT2rXsuiMNcGQFJ6FDNuGU5sSuAyYWto+ANvxGcp8FtJkr4AfvK0qQCSJN2JyHT9tLcGSJJ0DWI8aSBwEHhCluU3TnC+HliA8LLSgBzgMVmW3/H23idL45hPh8Osc74Wa3MUpJ/iMzte/flVPs/9HIDfjv8tZ6ef7bNrd1dcFRUUP/U3bB+LiEBMJhLnzydh3m0Bz8HWHvu2FLH6LRlHvZhPNmZ6X065OEMLKtDoFngjPn8FTgFWACUI4XnRM/6TAGwGHvHm5pIkXQG8BTyHCGK4GFgiSVKdLMvL2nnZP4F5iDDvHcDVwFJJkmyyLH/pzf1Plpbdbh1i3wqxzjgbDL7J97WjZAcv/PQCAHMy5jB3+FyfXLe7oqoqVcu/oOjxx3GXlwMQNnYsaX99BEtmZpCtEzgb3Kx7by/ZnkwFYVEmps8dRvpwrZS5RvfBm6zWDZIkzQBuAC4FMhC1e7YCnwKLZFl2eHn/J4D3ZFluDFJYIUlSPELojhEfSZIygF8D82RZftXT/I0kSYOB84HgiE9HnkRdDti/WmwP8s2cG7vLzkPrH0JRFQbFDeJPp/5JGwM4Ac6jRyn4y1+oXSPqHeojIkj63b3EXX110MOnGyk5XM3KRbupLKoDIH1YPNPmDiM8OjS8MQ0NX+HNPJ++siwfBhZ7lpNCkqSBCAFb0ObQMuBKSZIGyLJ8oM2xi4E6oFW3nCzLU07Wns7gaqzV0hHP5/CP4KgW2z4KNnj+p+c5WHUQo87I42c8jtmg/UAdD9XtpuKttyj+53OodeJHPXLaNFIffghTamgUz1NVlZ3fHmHDRzkoLhW9Qcepl2RomQo0ui3edLsdlCRpHaKbbJkPJpM2Bi/IbdpzPGsJaCs+ozznnytJ0hPAcM85D8my/O5J2tNpOvTT0BjlljYaok7+B29r0VbezHoTgPmj5zMk/kSxID0Xx8GDHH1wAfXbRYlyQ1IiqQ89TNSMc0PGS6yvdvDNG9nk7SoDICY5jBm3DCe5n+8nIPsaVVUpLS3FbrejKMovv0AjpNHr9VitVhITE/3+/fB2zOdK4GXEvJ6vEEL0WSfT6jTOiqtq0+5xDzjeNy8JkdbnNeBhhPDcCrwjSVKxLMvfdcKOwLC3McT65Lvc6px1PLT+IVRUhiUM45aRPSrCvUOoikLF0rcp/sc/miaLxl5xBcn3/Q5DTOhMyDycXc7Xr2dR5yl/MOTUVM68anCXKPamqir5+flUV1djsVgwBDGxqoZvcDqd1NTU0NDQQO/evf0qQN6M+SwEFkqSNBK4BrgCeBeoliTpI4QQfS3LstrBSzb+VW3Pb2w/3mOUGSFAF8my/DmAJEnfILyohUBoik/FQSj1OHg+EJ9ntj7DkZojmPQmHjv9MUz6wBcrC2WcR49y9I9/pO6HHwFRwrrX448RcdppQbasGbdLYeOnufy0SiQENVkNTL1WYvCk0OgG7AilpaVUV1eTkpJCfHx8sM3R8BHl5eUUFRVRWlpKUlKS3+7j9eOVLMu7gF3AHyRJGo/whuYA1wNFQK8OXsrmWbf1cKLaHG9JNeAGVrawR5UkaRXCAwpN9q0S67B46D3+pC71w9EfeNfTw3jX2LvIjAuNCK1QQFVVbB99TNHjj6PUiGSbMRdfTMofFmCIDp0uLFtJHSsX7aY4Tzj5KQOiOffm4cQkda3yB3a7HYvFoglPNyM+Pp7Kykrsdv/miT5Z3z4MEfGm8yyuE5/eisaxnkyEmNFiv+XxluxDJDQ1AS0j68wc60GFDo3VSjOngb7zXRPVjmr+tOFPAIxOGs2Nw270hXXdAldpKQV/+jM134r32pCQQNpfFhI1fXqQLWvN/p+K+XZJNg67G3Qw7rx+TLpoAIaOhuuHEIqiaF1t3RSDweD3MbzOlFQ4HeHtXIaY5GlDRKjNA9Z29DqyLOdIknQAuBz4qMWhy4B9siwfOs7LvgLu99z/dY89RkSY9brjnB98FAXyvhfbA6ee1KX+vvnvFNYWYjVYefT0RzGchJB1J6pWrKRw4ULcFSIGJmrGDFIX/hljCD2Ru90KP3y4nx3fiEwK4dFmzr15GH2GhI6NGhqBxJtQ638ihKEX0AAsR4zzfNGJ+T2NPAK8LklSBfA5MBshLFd77pmECMfOkmW5Spblbz0ZFp6XJCkS2AvcCQwAru2kDf6lOAvsnh7Efp0fc1h7ZC0f5QiNvmf8PfSP6e8D47o2bpuNwr8+StXnIruDPjqa1IcfInrWrJCJZAOoqbCz4r+7m1Lk9JZimXHLCG3ujkaPxhvP5y7EgP7DwAeyLFf/wvm/iCzLiyVJsgD3IcZscoEbWoRNz0R4OGcDqz1tlyNE60EgHpHq51xZlreerD1+IU/UgyEqDeIGdOoStgYbCzcsBGBi6kSuGXKNj4zrutSsW0fBHx/CVVwMQMQZZ5D22KOYUkKrTPihrDJWvZaFvcYJwPgL+jHpooHotbk7Gj0cr7Jay7Jc6GsDZFl+GRG+fbxji2kzoVWW5XpE19v9vrbFL+StF+t+p4naC53giU1PUFJfQrgxnEdOewS9ruuND/gKpbaWor/9ncp3xfOJLjyclN//ntirrgwpb0dRVLYsP8DmLw6CCpYII9PnDqP/SC3TeFflww8/ZMGCBaxZs4ZUH09OVlWVJUuW8Pbbb1NQUED//v257bbbuOiii3x6n1CiXfGRJOksIFuW5RJP02BPGpsTIstyh8d9uj2q2uz59Du9U5f4Ju8blucuB+B3E35Hn6g+vrKuy1G3ZQtHH1yA88gRAMLGj6fXE49jTk8PsmWtqa92sPLV3RzZI8agkvtHc/68EUTFW4NsmUao8vLLL/P8889z9913M2bMGNauXct9992HwWDgwgt9X3QyFDiR57MaUUBuaYv9E0WU6TzHtVHwRspyoNaj3Z0QH0VVeHbbswCc1us0rhh8hS+t6zIoDQ2U/PM5yhcvBlVFZzaTdM89xN94A7oQi7YqyKlkxaLdTQXfRp7dh9Mvy9QyUWu0i9Pp5LXXXuOaa67hjjvuAODUU0/l559/5s033+yR4nMT8EOL/ZsJ5XDmIKD+0rvRGOUWngBJ3tfX+fHoj+RV5QFw34T7QqpbKVDU7/qZow8+iGP/fgCsw4fT68knsAwaFGTLWqOqKju+OcwPH+5HUVRMFgNnXz+EQRNCawxKo2MoisJLL73Ee++9R0VFBaeffjoTJ0484Ws2btzIDTfc0O7xu+66i7vvvvuYdoPBwP/+9z9iY2NbtZtMJuo8uQi7I+2KjyzLS9rsLz7RhSRJMiBS3/QYXIpQH0N7g8eNXW7pp3ZqvOcdT4miCSkTGBQXWj+2/sZZWEjZa69R8dZSUV3UaCTx9ttJnD8PnSm0Mjo01Dn59o095G4XXm58rwjOnzeCuNSIIFsWHJxuhUKbfycodoTUGCumTs6f+vvf/84bb7zBHXfcwejRo/nqq694+ukTlysbPnw4777bforJ9saJ9Ho9kiQeTlVVpaysjA8//JANGzbwyCNeVanpUngTau0GrpNl+e12TrkReJbmnG3dnsaSCsctJqeqcNDj+fQ/w+trF9QUsObIGgCuGnJVp23sajgOHqR00SJsn3wKThEhZs7MoNeTTxE2YniQrTuWksPVfPXKz1SV1AMw5JRUzrpWwmQOre7AQOF0K0x/Zg15ZcF/Yu+XEM7X907xWoCqqqr43//+x80338xdd90FwJlnnklRURHr1rU/nTAyMpIxY8aclM0rV67kN7/5DQBTp05l9uzZJ3W9UOZEAQe9gJbTw3XAWZIkHe+xUw/8ih7WLXfCej6Vh6BKDIx3Zn7P+3vfR1EVEsMSmZY+7WTM7BLYs7MpfeUVqlesFBNzERmoE+bOJe6669BbLEG2sDWqqpL9fQFr39mL26VgMOo565rBDD0trUd2j3Yntm/fjtPpZNq01t+7Cy644ITio6oqbre73eN6vR79L9SNGjZsGG+++SayLPPcc88xb9483nij3cLOXZoTeT4liGqhjRFuKjDfs7TH8z6yq0vg8HzQjvtk1djlZomGlBFeXtfBB/s+AODywZd368ShdVu3Uvryy9Subf5Sm/r0IeHWW4i55JKQEx0QlUbXvC0j/yhmHkQnhXH+vBEk9Y36hVd2f0wGPV/fO6VLd7vZbGIycNucdb+UZHPTpk2dGvNpSd++fenbty8TJ04kMjKSBx54gJ9++omxY8d20Pquw4nGfJyeyqUDEF7Pt8DjwKrjnO4GSmRZPl4+tm6L0y0cveN6Po3BBumneJ3PbVXeKsrt5Rh0Bi4fdPnJmhlyqKpK7bp1lL7yCvVbmucGWwZlkjBvHtEXXIDOGJolBSoKa/nqlZ8pP1oLwMCxSZxzw1AsYaFpbzAwGfT0jQ8PthmdJi4uDhBZu9NbhPFXVlae8HXDhw9n2bJjCjA3kZycfNz2yspKVq9ezamnnkpKi0nSw4YNA6CoqKjDtnclTviN8eRXOwQgSdJNwNrjVBftsTR1ux3X8/GITydCrBuzVp+Tfg4pEd0nWkp1u6leuZLSV/5LQ3Z2U7t19CgS588ncurUkClnfTzkHwtY8/ZenA1u9Hodp16awehpfbVutm7G2LFjsVqtfPXVV4wbN66p/bvvTlyxJTIykpEjR3p9P0VRePDBB7nzzjubxnsAvv9e/IYMHvyL0yu7JN7U81nyy2f1LBraG/OpKoDyXLHtpfjI5TI/Ff8EwFVS9wg0UB0ObJ9+Stl/F+HIy2tqjzjtVBLmzSd88qSQ/gF32F2seVtm70bxBBoRa+G820aQltFjYmt6FBEREdx5553885//xGq1MmnSJFavXv2L4tNZ4uPjufbaa3nllVewWq2MHDmSrVu38vLLL3PFFVcwcOBAv9w32Jwo4MANXC/L8lLPvsIvBxSosiz3mP6HdgMODnpS6pjCRdlsL2gMrx4QM4BJqZNO2sZgotTVUblsGWWvvY6rsDkzU9S500mYN4+wTjwlBprivCpWLtqNzRPN1n9UIufcMISwSC0paHdm/vz5hIeHs2TJEl5//XXGjh3LAw88wMKFC/1yvwULFpCWlsayZct44YUXSE1N5e677+bWW0O3TNnJciKheAPY32a/R0Wz/RIOdzvdbvu/Eet+p4Ox4z9S1Y7qplQ6V0lXhbQ3cCLcNhsVS5dSvuQN3I395AYDMbNmkXDbrVgyQ78AnqqobP/mMD9+vB/FrWIw6jntskxGTvVvaWGN0OH666/n+uuvb9V2zTX+SeprMpm47bbbuO222/xy/VDkRAEHN7XZn+t3a7oYDpeIdmvl+SgK5Hwttged69X1Pt3/KfWuesKMYczO6Hrx/a6SEsqXLKHi7XdQasWAvM5sJvbyy4m/+WbMfXoH2cKOUVfl4JvFWRzKKgcgLjWcGbcOJ7GPFs2moeErTqqLzDPnZwYi2u1rWZa9qWTa5WmKdmvp+RTubM7nltnxKpqqqvKe/B4AswbOIsrctX7obJ99TuGf/4ziSQeij4gg7tpriL/hBox+rAPvaw5llfH161nUV4sJrsNOT+OMKwdjsvTMSaMaGv7CmwwHFuA5YKAsyzM8+z8AjYMa2ZIknSPLcrEf7AxJGjyej8XUQnwavZ64/hDf8YHCnMoccm0iSOGywZf5ykS/o9TVUfjoY9g+/BsKAqIAACAASURBVBAAQ2ws8XNvJO7aazFERwfZuo7jdils/CSXn1aJArrmMCNTfyVpudk0NPyEN57PnxGlsl/z7N8AjEEI0nbgGUSRt9t9aWAoU9sgxCfc3OJtzPGM92Se61U+t68PCdHqHdmbYfHDfGajP7Hv2UP+b+/FcUBE30dOmULak09g9MyT6CpUFtex6tXdFOeJ+ogpA6KZcctwohPDgmyZhkb3xRvxuRJ4VZblxhGxywAbcL8syy5JkgYiqpH2GPGpc4hexojGPF71lXB4o9j2ossN4Os8IT7T0qeF/IC2qqpUvP02xU8+hepwgMlEyn2/I+6GG0Le9rbIGwtZs1TG2eAGHYw/vx8TZw3A0MmElBoaGh3Dq0qmeEosSJIUDkwBPm8xznMI6FqPvCdJk+dj8byNB9aA6gaDGQac2eHrHKo6xN6KvQCc28+7IIVA47bZKHjoYapXiUQXpvR0ej/9NGEjvUshFGwcdhdr39nblCInIsbM9JuH00fqUR9hDY2g4Y34FAGNOcHPByzA8hbHRwFHfWRXl6DeKcQnorHbrXG8p99pYO54Ov1vDomuusSwREYljfKpjb6kbttP5N/3O1xHCwCInjmT1L8sxBAZGWTLvKM4r4qVr+7GVuyZuzMygXNuHKrN3dHQCCDeiM93wD2SJNmBXwO1wMeSJMUiCs3NA17yvYmhS22DcPrCLQZRQmGfR3xOostNrwu97h5VUSj77yJKnn8e3G50YWGkPvQQMZde0qW62VRFZce3h/nhIzF3R2/UcfplmYyc2qdL/R0aGt0Bb8TnHqA38A+gBpgny3KlJEmne9rWAn/xvYmhicutNKXXiTAboTgbqj2OnxfiU1hbyM7SnQBM7+edaAUCV0kJRx94gNoNoqitZfBgej/7DJaMjCBb5h11VQ6+WZLFod1i7k5sipi7o2Wi1tAIDt7kdqsEzpUkKQmwybLs8BzaDpwqy/JGfxgYqtQ5m+t2hJsNzV1u0b0haUiHr9PY5RZjiWF8ynif2niy1Kz/nqMPPIC7rAyA2GuuJuWBB9BbrUG2zDuK86r44sVd1FY2ADD09DTO1ObuaGgElc5MMi0HJkiS1A9wAId7mvAA1DW0EZ/GKLeBZ3sVYt0oPlP7TA2Zuj2q00nJ889T9t9FAOijokh79FGiz5sRZMu8Z++mQr793x7cTgWT1cDZ1w3R5u5odIoPP/yQBQsWsGbNmnZLYncWRVF49913Wbp06f+3d+bhURXZw347CwlZCCHsS9gtIOyyqIiggBpwkB+IyDiAg44IguKMCjjquH6KiIILgqgIjA6bDG4QFCGKGwgKA0IKkEBYwxIgIZCk093fH3U7dDqdpLvTSwL1Pk8/na5bde+5fTv33HPq1DkcPnyYhIQE+vXrx6RJk4ipYnOq7uKR8hFC3AbMQbnfTBi53oQQR4EJUsrPfS5hJSW34FIyh+iIMLig3DnUbOL2PrLystiaqerZVJYot4LDhznyj3+Qt125Aqt37kzDV1+tMqlx7FitNjZ9up9f16os2jXqVGfQ+I7Uauh+IIhGEyjee+89Zs2axb333su1115Leno6b7zxBvv27eP9998Ptnh+wZMMB72BlaiotyeA3ajy2W2ACcAnQoi+Usof/SFoZaOE5XPRUD7V3Q/V3ZCxAavNSlRYFNc0vMbXInpMdspajj31FNacHDCZSPjb36gzaSKm8MphkblLwcVCvv7gdw7sUO7Cxm3iueVv7YmMrlrnobkysNlsvPfee4wYMYJ//OMfAFx33XXEx8fzyCOPsHv3btq2bRtkKX2PJ5bPM8ABoLuU8pzjBiHEHOAX4ElgoK+Eq8w4Wj5R1cLg4hn1oXqtUkaUxJ7V4IbGNxARGtxy0WdX/pdjTzwBQGhCAg1fmU5ML88L4QWbsycusHrO/zhzXOWY63hTY3oNa0WIXjSq8QCr1crcuXNZtmwZZ86coVevXnTv3r3MMZs2bfKqjHZubi6DBw8mOTm5WLu9jk9GRsYVr3x6AM85Kx4AKWW2EOJ9YKrPJKvk2LMbRIaHEGriktvNTcvnXP45fj72MxD8KLfcH3/k2NNPA1C929U0fv31KpUM1M6h3Vmsnb+T/AuFhISa6PNnQbteDYMt1pWHxQzZlWDJX42GEOqdtTtjxgwWLVrE+PHj6dSpEykpKcycObPMMUlJSSxdurTU7aXNE8XExPDkk0+WaF+3Tj2ctqoCJUi8wZeF32yAx1daCDESZTG1QFlWL0kpF7k5tgmwE5ghpXzB02NXhIsFKsw6MjwUCnLBqrIgu6t8Fu9aTKG1kOph1endyP1sCL4mT0oOT3oICguJEIImc+dWuUWjNpuN/204zA8r9mGz2qgeG07yuA40aFUz2KJdeVjM8FZ3OJMebEkgvjlM/MVjBZSdnc3ixYsZO3YsEydOBKB3795kZmaycePGUsfFxMTQuXPnColsZ/v27bz77rv079+fllVsWYO7eOKL2ATcK4QoMWMrhIhF5XX7xZODCyGGAx8BXwFDgFRgoRDiDjfGmlBJToOaOjnEZLo03wMQVb7yOX3xNIt2Kf06qt0oosKj/CVemZgzMzl0/zisubmE1atHk3lVT/FYzFY2/DuN75ftxWa1UbtJDMOnddeKR+M127Ztw2w2069fv2Ltzm4xZ2w2G4WFhaW+rFarW8ffunUr9913H40bN+aFFwL6TB1QPLF8nkVlOdgphHgL2GO02wMOGuN5UtGXgGVSykeMz2uFELWA54EV5Ywdbxw7+Njne8Aty+e9He9xsfAicRFx3JN0j//kKgPL+fMcGvcAhZmZhERH0+TdeYT7OHzU31zILmDN3B0c3688wa2urstNY9oSXk2v3wkaoeHK2qjCbrdz59TvqVat4vO3dcpxRW/evNmrOR9HVq9ezdSpU2nWrBnvvfce8VUsQ7wneLLIdKMQYijwNjCDSyW1TcAxYISUcoO7+zOyYLcEpjltWgHcKYRoLqV0absbY6cDw4E17h7Tb9jne0whEBFXZtej54+yVCq/8L3t7w1K0Tib2cyRhyeTn5YGYWE0mj2bSCECLkdFOJmRw+p3/sf5M2rhaM/bW3D1rU11mpzKQGg4xDcNthReY7/hnzp1isTExKL2s/aS8KWQlJTEihWlPzPXrVu3zPELFixg+vTp9OjRg7fffpvY2Ms7+4ZHcz5Sys+EEF8CXYHmKMVzANjqRRVTu9Uindr3Ge8CKKF8hBAhwIcoiylFVIabpt3yiawJIWV7Mudsm4PZaqZu9bqMbOOfevBlYbPZOPbss+T+8AMADZ59lpjrq1ZU294tmaxfuJtCs5XwiFD6/7UdLTpXvQAJTeWkS5cuREZGkpKSQteuXYvaN2wo+9k6JiaGDh06eHXM5cuX8/LLLzNw4ECmT59OtWqXf5JbjwMOpJQWIUQ6YEWVz073sny23UTIdmrPMd5Lm8uZjApO+JMXx/QP9jmfqLLDrP84+wef71frcB/o/ACRYYFPU3N63jzOrfgEgNoTxlNz2NCAy+AtNquNTZ/vZ+saY+Fo7UgGju9IQqOqNU+lqdxER0czYcIEZs2aRWRkJD169CA1NbVc5eMtp0+f5sUXX6RRo0bcfffd7Nq1q9j2xMTEEi7AywFPMxz0Bl4GeqKsHgCLEOIbVFG5nR7szj7eVkp7idk5ocycF4BhrkK+g0bRGp+y/bNv/fYWVpuVxNhEhrQaEgDBinPus884OWs2AHG3D6Z2Of7nykRBXiHrFuwiffspABqJmtz6tw5ExuiFoxrfM27cOKKioli4cCELFiygS5cuTJkyhWeeecbnx9q4cSMXL17kyJEj3H333SW2v/LKK9x+++0+P26w8STDQV9gLaqUwtvAXiAUuAq4G/hBCNHLAwVkVx7OFk6s03b78UOBhcBy4GshhKPsIUKIMC8tsIpzoXzls+PkjqJFpZO6TAp4Hrfcnzdx9J9qLUHUNdfQ4Pnnq8z8yLmTF1n9zv/IOpoLQIe+jek1vJWuNqrxK6NGjWLUqFHF2kaO9L2rfMiQIQwZEviH0WDjieXzAmp+p5eU8pTjBiHEc8DPqOg1d91h9rmeVsAOh/ZWTtvtNEFZXD0B55CSZ41XcO6mRal1SjeNZ/+mLI42tdpwc7PAJujM37uXw5MmgdlMROtWNH5jNqYq4lM+nJZFyvyd5OeqhaM33HUVSb2rVp45jUZTEk8eHTsD7zgrHgApZSYq4egN7u5MSrkPFVDgvKZnGLBXSpnh1H4U6O7iBfCOw9+B50LZcz4/Hf2JTcdU1uuHujwU0IJx5hMnyBg3DmtODmF16tBk3jxCawR1aZRb2Gw2dqQe5rM3tpOfW0j12HBun9xFKx6N5jLB0zLaZeWij6Rk8EB5PAcsEEKcAb4ABgN3AncBGLWDWgK7pJTZwBbnHRjRbkellCW2BYwyLB+bzcYbv74BQNe6Xbm+0fUBE6vw5Eky/jqWwqPHMEVF0WTeXMIbVv50M4VmC98t2cPuH1S57oTGMQwc34EaCdWDLJlGo/EVnjyCvwg8LIQo4VYTQvRERaE958nBpZQfoham3gKsAvoCo6WU9gRJg4CfUKHdlZciy6fknM83Gd+w87SaBpt89eSAzbOYT5zg4Jh7KPjjD0zh4TSePYvIdu0CcuyKkH36Iitn/FqkeFp2rcOwx67WikejuczwxPK5FjgBrBJCpAG7UMXkWqJcXvnASCNXmx2blLJfiT05IKWcB8wrZduHqDU9ZY0P/qx5KZaPxWrhzd/eBKBP4z50qdslIOKYT5wgY8w9FKSnY6pWjcZvvUlM7+Dlj3OXjF2n+er938nPLcRkgmuGtKTLzYlVJjBCo9G4jyfKpz8qLDoDiAK6OWyzz88095FcVYYQmwUuGiufneZ8dpzawf5z+wEV4RYIzJknyBgzhoIDB5TiefutSq94bFYbW1MOsunz/WCDyJhwbr4viSZtLr+1DRqNRuFJep0rTrG4QywXKFqq5GT5pGWlAdAwuiGilv8zMZgzM8kYPYaCgwcNxfM2Mb0DN8fkDfkXzKz7cDcH/qfiWOo2q8Gt97cntlbgF+BqNJrA4cuSClckcUUJGShh+ew5o3KvXhV/ld/lMB8/zsExYzAfzMAUEaEUTyVPm3P6yHnWzN3BuZMXAUjq3ZDed15FaLhev6PRXO5o5VNBajoqn+qulU/r+NZ+lcF87BgHx9yDOUMpnibvzCH6uuv8esyKsmfzcTYsTqPQbCU0LIQ+f76KttdV/kg8jUbjG7TyqSBFlk9YJFS7VJfHarMWKR9/utzMR48qxXPoEKbISKV4rr3Wb8erKJZCKz98so8dGw4DEJsQSfK4DtRJvLwz+Go0muJo/0YFibOdV384WT1Hco5wsVC5k/zldjMfOcLB0WMuKZ65cyu14sk9m8+q134rUjyJSbW484nuWvFoqgQrV65ECMHx48f9epzdu3eTlJTk1nE+/fRThBAlXs8959Gql6CgLZ8KUmT5RCUUa7dbPZGhkSTGJjoPqzAFh4+QMWYM5iNHMFWvrhRPzx4+P46vOLr3DCnzf+didgEA3QY1o/ug5oSE6DBqjcbO/v37GTduHIWF7qWpTEtLo2nTprzyyivF2mvXru0P8XyKV8pHCNEQlWstDbgIFEop3asRe5kRb0/q4LTAVJ5Rqela1WxFaIhvK2uajxwhY/RozEePYoqKInHeXKK6By+7UFnYbDa2f3OIH1f+gc1qIyIqjP73tKNZx8r/z6HRBIrCwkKWLl3KzJkzCQ93P+mwlJKkpCQ6d+7sR+n8g6clFXoBb6DyvAEMMPbxgRDi71LKZT6Wr9JTGyOjdUzxEtRFkW61fOtys9lsHH3yyUuK5915RHXrVv7AIFCQV8iGf6exb8sJQKXJSR7Xnrg6UeWM1GiCi9VqZe7cuSxbtowzZ87Qq1cvupfzgLdp0yavy2hv3bqVV199lXvvvZd69erx5JNPuiVnWlpamceszHhSUqE7sA44BMxCpdMByALMwMdCiBwpZfDLWgeQOjZD+cQWT3vnrzDr8xtSufDTzwA0mvFKpVU8x/ef4+sFu8g2wqhFz/r0uVsQXs23VqCm8mG2mjlx4USwxaBuVF2vS5fMmDGDRYsWMX78eDp16kRKSgozZ84sc0xSUhJLly4tdXv9+vVL3dayZUvWrVtHQkICK1eudEvGEydOcPr0aXbt2sWtt97KoUOHaNy4MePHj68SJRo8LamQDlwNRAOPAEgptwghOgE/AE8AV5TyKbJ8YhsUteWaczmUcwjwrfKxFRRwwvDtRvfqRcxNN/ls377CYrGydfUBtqw5iM1qIzQshF53tKJ9n0Y6Tc4VgNlq5vZVtxf9/oNJk9gmfDrkU48VUHZ2NosXL2bs2LFMnDgRgN69e5OZmcnGjRtLHRcTE+O1+8ubOZq0NLWI/fDhwzz22GNERESwatUqpkyZgsViYdiwYV7JEig8ze32vJTyohCimN9ESpkthHgXDxOLXg5ccrtdsnz2ntlb9Lcvlc+Z//yHggMHICSEulMer3Q387OZF/h6wS5OHFDzYAmNYhgwtp0uc62pUmzbtg2z2Uy/fsXTUiYnJ5epfGw2GxaLpdTtISEhhIT4LsC4ffv2zJ07l+7duxMTo/7Hrr/+ek6fPs3s2bMvK+UDKnloaURyhYVuh1NIvD3aLfaSSW13udWPrk9cRJxPjlV45gwn354DQM0RdxJ5lf+zJriLzWZj1/dH+X75XgoLrGCCzv0TuWZwC52t4AojPCScT4d8WqXdbufOqSLKtWoVXz5Rp06dMsdt3rzZ6zkfb6hVqxY33nhjifY+ffrw448/kpWVVeIcKhOeKJ9NwJ9RAQfFEEJEA/cBv/hIripBHc5e+hBTUvn40uo59dbbWLOzCYmNpY4Pf8AV5UJ2ARv+nVaUmy0mPoJ+Y9rSWCcFvWIJDwmnUUzVLfoXH68iV0+dOkVi4qVlEmfPni1tCKDmfFasWFHq9rp16/pGQIPffvuNffv2MXz48GLt+fn5hIWFERtbudfPeaJ8ngZShRDfAp+ismn2FEK0Bx4CmqJq81wx1DU5/BgdAg5+P/U7oEpm+4L8P/7gzJIlANQeP56wSvI0c2DHKdYv2s3FHDMArbvV5YaRgsho7yZ5NZrKQJcuXYiMjCQlJYWuXS+VEtuwYUOZ42JiYujQoYO/xSti27ZtvPzyy3To0IE2bdS9xmq1snbtWrp27epRyHYw8CSr9U9CiNuAucCrRvOLxvsxYISUsuyrc5lRz2TM91SLgQj1lFFgKSDtjJoI7Fi7o0+Okzl9OlgshDdNpNZf7vbJPiuCucDCjyv2sfO7IwBUiwylz58FV/UoPZpHo6kqREdHM2HCBGbNmkVkZCQ9evQgNTW1XOXjb7KyssjIyKBVq1bExMQwdOhQFi9ezMSJE5k8eTLR0dF8/PHH7Nmzh48++iiosrqDRw55KeXXQCtU8bgRKDfcdUBTKaV78YGXEbVNyjdMzCVzOi0rjUKrWp2cVDupwsc4v3Ejud+pSc56jz2GqVq1Cu+zIpw4mM2yF38pUjwNW9dkxFM9tOLRXFaMGzeOJ554gtWrVzN+/Hj27NnDlClTgipTamoqI0aM4PfflWclLi6OxYsX07FjR1566SUmT57MhQsX+PDDD+nUqVNQZXUHjzMcSCltwFbjdUUTjVrDQkSNorYdp3YAqoZP7eoVW8VvKyxUVg8Q1bMnMf3KLArrV6xWG7+mHOSXL9KxWm2EhJroObgFnQck6hQ5msuSUaNGMWrUqGJtI0eOLKW37xg6dChDhw51q71Ro0a89tprfpfJH3iyyHS9O/2klJVv8YmfqI7KU0b4pcjznad2AtC+dvsK7//MsmUU7PsDTCbqTZ0StNDq7FMXWbdgF8f+UJZefP0oBoxN0glBNRqN13hi+bSgqGRnEaFAbVSY9QFgp2/EqhpUN9mVT/WiNrvy6VC7YhOPlnPnOPXGmwDUvGMYkW3bVmh/3nJw52nWvrcTc55av9DhxsZc938tCdOZCjQaTQXwJOCgmat2IUQocDvwHpcCEa4IIu3Lngzlcy7/HAeyDwAVt3xOzZmD5exZQqKjqfPwwxXal7fs33aStfN3YrXYiKpRjX5j2pKYlFD+QI1GoymHCpdUkFJagJVCiJ7AdFQmhCsCZ7fb76fVRGCIKYR2Ce283u/5b78la9FiABLGjSMsCOnR9209wdfv/47VaqNWw2gGP9yZ6LiIgMuh0WguT3y5/HwvUPlDLHxIdVNxy8fucmtZsyVR4d5lbi7IyODIY4+DzUb1Tp1IuGeMT2T1hD2bj/PVezuxWm0kNI5hyCNdtOLRaDQ+xSfF5IQQEcBfgODn1AggRZZPtWgAdpxUkW7ezvdYL17k8KSHsGZnE5qQQKM3Zgc8tDrtp2N8s2g32KBOYiyDH+6sF41qNBqf44totwhAAPHAv3whVFUhwq58Qqthtpj5JVNlF+pcx/PMtjabjWNP/4t8KSE0lEavv0Z4vXrlD/Qhv288QurHEmxQr3kN/jSpExFRWvFoNBrfU9FoNwALqqLpf4A5vhCqymEyse3kNnLNuQD0atTL412c+fdHZH/+OQD1Hn+M6B6BLYm9I/Uw3y1ROekatIrjtomdqBapq6xrNBr/4MndpZuU8pSvBRBCjASeRCm3A8BLUspFZfSvDzwP3AzUAiQwXUq53NeyecL3R74HQMQL6kZ5lkDwwtatRYtJawwcSHyAKxNuW5fBDyv2AdBI1GTQhE6ER+hQao1G4z88CTj4VQjhXm1XNxFCDAc+Ar4ChgCpwEIhxB2l9I8AUlDlu58GhqIyLSwzlFjQsCuf6xtd79E4c+YJDk+eDIWFRLRuTYMXng/oYtKtKQeKFE+TdrUY9KBWPBqNxv94YvnUATJ9fPyXgGVSykeMz2uFELVQlo2r3OTJqIi6HlJKe/mGr4UQicAUlOsv4JywXCwqo+CJy81WUMCRyZOxnDxFSGwsjd96k5Ao76LkPMVms7Fl9QE2f54OQNMOCdx6f3vCwrXi0Wg0/scTy+cj4H4hRDNfHFgI0QJoCXzitGkF0EYI0dzFsGzgXWCLU3uasa+g8EOe0snR4dF0rut+sMGJmTO5+NtvADR8ZTrVmjb1i3zO2Gw2Nn26v0jxNO9Um+RxHbTi0WjKYOXKlQghOH78uF/2/8UXXzBo0CA6duxIcnIyq1atKrP/1KlTEUKU+rKzZcsWl9vHjRvnl/NwF08sHyvQBtgrhNiHCqt2rhlrk1K6m/3SXuxGOrXvM94FkO64QUq5HigWdSeECAcGAb+7eVyf832++jFe0+AatysnFp4+TdbHylCrPWE8sS4qEvoDm83GDyv2sf2bQwC0urou/ce2IzRUVxzVaILFmjVrePTRRxk9ejS9e/dm3bp1TJkyhcjISG699VaXYyZMmMBdd91VrO3gwYNMnTqVO++8s6hNSklUVBQLFiwo1rdGjRoEE0+UzwDAHnAQCSSW0dcd7PWls53ajbrUuPvNTAdao+aMgsKv+acBuK7hdW6PObdqFZjNhNSoQcL99/tLtGJYrTa+/SiNXT8cA+CqHvXoN6YtIVrxaDRB5bXXXiM5OZknnngCgN69e3Pu3Dlmz55dqvJJTEwsVmnVYrHw/PPP06ZNG/75z38WtaelpdG6dWs6d/Z8CYg/8SS3mys3WEWwz6o7h2/b261lDRZCmFCK5xFghpTyU9+K5x55JhOnrHkAtIhr4dYYm83G2eVqSitu8GBCIiP9Jp8di8XKugW72LdFrQNO6t2QPiMFJl0OQeNjbGYz5szgrzcPr1cXk5fVPK1WK3PnzmXZsmWcOXOGXr160b179zLHbNq0idFlRKpOnDiRSZMmlWg/dOgQGRkZ/P3vfy/Wfsstt7BmzRoOHTpEkyZNypV5yZIl7Nq1i6VLl1LNYXH67t27aRukxMRlUaryEUJ8AMyTUm7y07GNSmwlLJxYp+0lMKLePgTuQimex30unZscD700T9IwpqFbYy5u2ULBgQMA1BzuMrDPpxSaLax9dycHdigLrfOARK4b2jJoJRo0ly82s5k/Bt2GOSMj2KIQnphIyy+/8EoBzZgxg0WLFjF+/Hg6depESkoKM2fOLHNMUlISS5cuLXV7/fquCy7u378fgObNiz/fNzXmgNPT08tVPrm5ubzxxhvcfvvtdOx4qYKy1Wpl7969xMfH83//93/s3buX2rVrM3r0aP76178G9R5QluVzD7AO8Jfysc/1tAJ2OLS3ctpeDCFEDeALoBcwWUo520/yucWxMKV8Qkwh1Imq49aYM8vVkqTIjh2JdJgY9AcFeYWsfmcHR6Qq+d3jT83pNrCZVjwaTSlkZ2ezePFixo4dy8SJEwHlBsvMzGTjxo2ljouJifHKtZWTk1M03pHoaJW26/z58+Xu45NPPiE7O7tEEEF6ejp5eXmkp6fz97//nfj4eL755hteeeUVzp8/z0MPPeSxvL4iaEvYpZT7hBDpwB3Afx02DQP2SilLPDoZ5Rs+Ba4B7gr2wlKA42HqK6xTvY5bwQaWc+fIWfsV4H+rJy/XzBdvbSczXU2rXT+8NZ36lW++azTeYgoPp+WXX1Rpt9u2bdswm830c6ocnJycXKbysdlsWCzOMViXCAkJISSk5PyqzaZmHpwfCO3trsY489FHH9GvX78S1lO9evWYP38+bdu2pU4d9XB87bXXkpeXx/z58xk7dmwJpRcogp0/5TlggRDiDMqaGQzciXKnIYSogwqh3iWlzAYeAPoC84BDQohrHPZl86OL0CURJjNHDeXjrsvt3GefY8vPJyQqiriBA/0m24XsAj6bvY3TR86DCW78Sxva9XJPRo2mIpjCw6nWuFGwxfCac+eUx79WrVrF2u0379LYvHmzV3M+sbFqpsHZwsnNzS22vTTS0tI4cOAAjz764TdLOAAAHwFJREFUaIltMTEx3HDDDSXa+/bty/Lly0lPT6dDh4oVvvSW8pRPbyGERwqqrNQ4Lvp+aMzfPArcB+wHRksp7Y7TQcAC4EZU9oNhRvs44+WIhQAr02jyitxu9aNd+3MdUYEGylirMWgQIYZZ7WtysvL4bPY2zmZeICTERP+x7WjdLbBJSjWaqkp8fDwAp06dKhZNdvbs2TLHJSUlsWKFq7Xxirp1XafdslsrGRkZxdbnHDx4sNj20khNTSUqKoo+ffqU2CalZOvWrQwfPpxwByswL08FSdnPNRiUd7O+33i5gwkVuea28gGQUs5DWTKutn2ICiywf77Jk337myjyitxuDaIblNs/7/dd5O9RmRBq3jncLzKdPXGBz2ZtIycrj9CwEG69vz3NOga+GJ1GU1Xp0qULkZGRpKSk0LVr16L2DRs2lDkuJibGKyuiadOmNG7cmJSUFAYMGFDU/tVXX9GsWTMaNizbY7Ft2zbat29fLMLNzsGDB3n22WepV69eMTfi6tWrady4MY0aBc9CLU/5vAv8HAhBqiLRpjyOhalCcu4on5yv1FxPtRYtiGxfsTLbrjh95Dyfzd7GhewCwiJCGTShI41F8J5sNJqqSHR0NBMmTGDWrFlERkbSo0cPUlNTy1U+FeHBBx9k2rRpxMXF0bdvX9avX8+aNWt4/fXXi/pkZWWRkZFBq1atis3T7Nmzx6XVA8q91r59e5566imysrKoX78+n3/+OevXr+fNN9+stNFuABullB8HRJIqSHXyyQxVPwJ33G45X38NQGz//j6/6Bm/n+ar938n/0IhEVFh3DaxE/VbxJU/UKPRlGDcuHFERUWxcOFCFixYQJcuXZgyZQrPPPOMX443dOhQCgoK+OCDD1i+fDlNmjRh+vTpDHSYF05NTWXatGksWrSInj17FrWfPn261GwF1apVY/78+cyaNYu33nqLrKwsWrduzVtvvUX//v39ci7uEuyAg6qLzUZhSAH5RiRKvaiy51Ty//iDgnSVLSjWwbSuuBg2fl17kJ8/3Q82qB4bzuCHO1O7cdmTlBqNpmxGjRrFqFGjirWNHOm/5Pl33XVXiXQ5jgwdOpShQ4eWaN++fXuZ+61VqxbPPfdcheXzNVr5eEmIJY+T4ZdCIOtFl618cr5eB0BYgwZEtk/yiQwFeYV8s3A3+387CUDdZjVIHteemHj/Z0zQaDSailCW8lkI/BEoQaoaYYUXyDSyG4SbwoiPKHtuJWedUj6x/fr5xOV25ngua+bu4MzxCwC07dWAG+66Smem1mg0VYJSlY+U8q+BFKSqEWq5UBTpVq967TIVivnoUfJ27gTUfE9FSd9+knULdlGQZyEk1ETvEVeR1Luhzlqg0WiqDNrt5iWOlk95wQZnP1kJQGjNmkR1u9rrY9qsNjZ/mc6WLw8AEBVXjeRxHXRggUajqXJo5eMloYUXyDQWmNYrI8zakp1N1iK19KnmiBGYwrz7yvMvmPl6wS4OGslBG7SM45b72xMdF+HV/jQajSaYaOXjJWGFFzhpWD51ywg2yFq4CGtODiFRUdS6Z4xXxzp95Dxr5u7g3MmLAHTo04hew1sTGqbr8Gg0mqqJVj5eElp4gfNGmHVsNdcx9o5WT/yoUYR5kcpi39YTfLNoN4X5FkLDQujzZ0Hb68pf0KrRaDSVGa18vMRks3DBKMQWFR7lsk/WosUVsnp2pB7muyUqHU9MfATJD3SgbtPglr7VaDQaX6CVTwW4YFKWT1RYSeVjyc4ma+FCwDur59e1B/npvyrSvUHLOJIf6ED12JK5mzQajaYqopVPBcg1LJ/o8JLZqb21emw2G5s+3c/WFJXRtkm7WiSP60B4hF6/o9FoLh/0jHUFyDXmfJyVj/nYMbI+/BDwzOqxWW18v2xvkeJp0bkOg8Z31IpHo6kErFy5EiEEx48f98v+v/jiCwYNGkTHjh1JTk5m1apV5Y45efIkTz75JDfeeCNdunRh6NChrFmzplif48ePI4Qo8brtttv8ch7uoi0fLym0WSg0FnVWNzJbA9isVo5OnYb1/HlC4+PdtnqsVhsb/p1G2o/HABA963PT6DaEhOrnA43mcmfNmjU8+uijjB49mt69e7Nu3TqmTJlCZGQkt956q8sxBQUF3HfffeTk5PDQQw9Rt25d1q5dy+TJk7FYLEXKJS0tDYD333+/WDbsyMjgpuHSysdLbNiK/g4xXVIQWQsXcWGTKqja4MUX3LJ6LIVWvv5gF3/8qkoPJ93QiD53XYUpRGcs0GiuBF577TWSk5N54oknAOjduzfnzp1j9uzZpSqf7777jrS0NJYvX07Hjh0B6NWrF0ePHmX+/PnFlE/t2rW5/vrrA3MybqIfq31IntzDyddeA6Dm8DuIvan82neWQitr5u0oUjxdBiTSZ6RWPBpNMLFarcyZM4e+ffvSqVMnJkyYUFReuzQ2bdrk0r1lf7355psuxx06dIiMjAxuvvnmYu233HIL+/fv59ChQy7HRUdHM2LEiBIF7Fq0aEFGRkbR5927dxerkFpZ0JaPj7AWFHD08cexmc2EJyZSb+pUt8bt/vFYUdaCnoObc3VyM52jTVOlsVis5J7JD7YYRMdHEOql23rGjBksWrSI8ePH06lTJ1JSUpg5c2aZY5KSkli6dGmp2+vXd52Ga//+/UDJctlNmzYFID09nSZNmpQYd+2113LttdcWazObzXz77be0bt26qC0tLY2EhARGjhzJzp07iY2NZdiwYTz00EPFSmsHGq18vMTq4HYzmUycensO+VJCSAgNp79MSHTJCDhX7P0lE4DW3evRbWDZtdo1msqOxWLl42c2kW1k4wgmNepU58/P9PRYAWVnZ7N48WLGjh3LxIkTAeUGy8zMZOPGjaWOi4mJoXPnzh7LmZOTUzTekWjjHnL+/Hm39/Xqq69y4MAB3n77bQAuXrxIRkYG586d47HHHuORRx7h559/5t133+XEiRNMnz7dY3l9hVY+XnLemlf0d+wfmZyePx+AhPvuI6pLF/f2cSafo/vOAirAQKPRBJ9t27ZhNpvp169fsfbk5OQylY/NZsNisZS6PSQkhJCQkorQZlMPss4eD3u7qzGu9jFjxgw+/PBD7r333qIqpaGhoXzwwQc0atSIxMREAHr06EF4eDizZs1i/PjxNGvWrNz9+wOtfLwkx6rq6IRabFiemwVWKxGtW1N74oNu7+OPX0+ADSKiw2jc1vPUOxpNZSM0NIQ/P9OzSrvd7HM7tWrVKtZep06dMsdt3ryZ0aNHl7p94sSJTJo0qUR7bKyqOuxs4eTm5hbbXhoFBQVMnTqVL7/8knvvvZfHH3+8aFu1atVKuOYA+vbty6xZs0hLS9PKp6qRbSifVsdtFO5X5bEbvPQSIdXcz0Kwd4tyubXsUtdr37RGU9kIDQ2hRu3q5XespMQbEaqnTp0qshYAzp49W+a4pKQkVqxYUer2unXrumy3z/VkZGQUCww4ePBgse2uOH/+POPGjePXX3/liSeeYMyY4ks7Dh06xI8//siAAQOKKdO8POW5ifci36Sv0MrHS/IwA1AvxzCZo6Ko7mZ5bEuhlV/XHiQzPRuA1t1c/yg1Gk3g6dKlC5GRkaSkpNC1a9ei9g0bNpQ5LiYmpkTkmTs0bdqUxo0bk5KSwoABA4rav/rqK5o1a0bDhg1djrNYLIwfP57t27cXhWo7k52dzdNPP01+fn4xq2z16tXExMTQrl07j+X1FVr5VJBYZQAR5mSil0bmgWw2LN7N6SPKpK7bNJaGV2mXm0ZTWYiOjmbChAnMmjWLyMhIevToQWpqarnKpyI8+OCDTJs2jbi4OPr27cv69etZs2YNr7/+elGfrKwsMjIyaNWqFTExMSxZsoTNmzczYsQIGjRowLZt24r6mkwmOnXqRFJSEjfddBOvv/46VquV1q1b8+2337J48WKmTp1arkvPn2jlU0FqGMontBzlk3+xkM2f7WdH6mFsNjCZoFP/RHr8qTkhek2PRlOpGDduHFFRUSxcuJAFCxbQpUsXpkyZwjPPPOOX4w0dOpSCggI++OADli9fTpMmTZg+fToDBw4s6pOamsq0adNYtGgRPXv2ZO3atQAsXbq0RIh3aGgou3btAmDmzJnMmTOHxYsXc+LECRITE3n++ecZPny4X87FXUz2iIorFSHE2djY2LgtW7Z4NO6d/05jTvYXPPJZIdf+DjUGJtPIWGDqiM1mY8/mTH74ZB8XswsASGgUzY2j2lKvmS6PoKm62Ock7OtRNJcP5V3bbt26kZOTc05KWdPbY2jLp4I0VokJiBBtSmw7feQ83y3Zw9G9aqIyLCKU7gOb0alfE12FVKPRXNEEXfkIIUYCTwItgAPAS1LKRWX0jwGmA8OAGOA74GEp5V7/S3uJamEmQi02GqjkBES2uRSlkpdrZvPn6ez87gg2q7IsW3atQ687WhNbK7jJ/DQajaYyEFTlI4QYDnwEzAZSgCHAQiHEBSllaTGLS4HuwGNADvAvYIMQIklKWXbyJR/SMK46zXdAmFV9jmjTFlDh09/9Zw95uSoarma9KHqPaE1iu4RAiabRaDSVnmBbPi8By6SUjxif1wohagHPAyWUjxDiemAgkCylTDHaNgLpwAMoiygghJigeaayakIbNiCXGPatTmfTZ2rNT3hkKN0HNafjjY21i02j0WicCNpdUQjRAmgJfOK0aQXQRgjhamXVzShr52t7g5TyJPAtSikFlKh8OB3fho0tHuKjf/1cpHgatIrj7mevocuARK14NBqNxgXBtHzsM/TSqX2f8S5QFo3zmH1SSucESvuAEb4VrxxO59M65zG2d7q0AjoiOowWnevQ+86rdPVRzWVPSEgIZrM52GJo/IDFYvF7xutgKp844z3bqT3HeHcVhxznor99TEDjlsNPNOR87CXFc8fUbtRNjNV1eDRXDJGRkZw/f56srKwSedA0VZesrCzy8/P9vgA1mMrHfpd2Xmhkb7eWMsbVwiRTKf39xvVj7uX04XeISGhNr+F9SGgYU/4gjeYyonbt2uTn55OZmcnZs2cJDdXWflXHYrEUKZ7atWv79VjBVD72yDRniyXWabvzmBYu2mNL6e83qkVEMPy5yYE8pEZTqTCZTDRq1IhTp06Rl5eH1RrQ5z+NHwgPDy9SPP4uahlM5WOf62kF7HBob+W03XlMfyGESUppcxrjqr9Go/EjJpOp3FIDGo0rghaKJaXchwoouMNp0zBgr5Qyo+QovgJqAv3tDUKIOsANwDo/iarRaDQaHxPsdT7PAQuEEGeAL4DBwJ3AXVCkWFoCu6SU2VLK74QQqcASIcTjQBbwDHAWeCfw4ms0Go3GG4K6CEVK+SFqcegtwCqgLzBaSmlP0ToI+Ano6jBsKPAZ8CrwIXAY6CelPBMQoTUajUZTYXRWay+zWms0Gs2Vii+yWuvl9xqNRqMJOMGe86kM1MjJyaFbt27BlkOj0WiqBDk5OVDBhf1a+ajFqSE5OTmuMidoNBqNpiQ1qODC/it+zkej0Wg0gUfP+Wg0Go0m4Gjlo9FoNJqAo5WPRqPRaAKOVj4ajUajCTha+Wg0Go0m4Gjlo9FoNJqAo5WPRqPRaAKOVj4ajUajCTha+Wg0Go0m4Gjlo9FoNJqAo5WPRqPRaAKOTixaBkKIkcCTQAvgAPCSlHJRGf1jgOmoUuAxwHfAw1LKvf6X1jd4cc71geeBm4FagASmSymX+19a3+DpOTuNbQLsBGZIKV/wm5A+xovrHAJMA+4FGgD7gBellEv8L61v8OKc6wCvoIpdRgI/Ao9Upf9nO0KIzsAvQHMp5eEy+gXsHqYtn1IQQgwHPgK+AoYAqcBCIcQdZQxbCgwHpgCjgUbABiFEnH+l9Q2enrMQIgJIAQYAT6OqzG4Flhn/6JUeL6+zfawJ+IAKppYPNF6e8yzgKeAt4DbgZ+BjIUSyf6X1DV78tk3Af4FkYCowCqiP+n+OD4TMvkIIIYAvcM/YCNg9TFs+pfMSsExK+Yjxea0QohbqKX+Fc2chxPXAQCBZSplitG0E0lGlwqcHROqK4dE5o/4xOwE9pJS/GG1fCyESUT/e//hbYB/g6Tk7Mh5o40/h/ISnv+2WwIPA/VLK943mb4QQVwG3AmsCIHNF8fQ6twZ6AWPs1pEQYjfwBzAYWOh/kSuGECIMuB94GTC70T+g9zBt+bhACNECaAl84rRpBdBGCNHcxbCbgRzga3uDlPIk8C3qglZqvDznbOBdwLkGeZqxr0qNl+fsOHY68Df/Seh7vDznIcAFoJiLSkrZR0r5sF8E9SFennOk8Z7j0JZlvCf4VkK/cT3KbTgT9TBYHgG9h2nl4xr706x0at9nvItSxuyTUlpcjHHVv7Lh8TlLKddLKcdJKYuKQgkhwoFBwO9+kdK3eHOd7fMfH6KepFP8I5rf8OacOxr9BwghtgshCoUQe4UQI/wlpI/x5rf9P2AD8LQQoo0x//MGcB5Y5S9BfcxuoIWU8lmg0I3+Ab2Habeba+z+TefqpvanIFc+/jgX/e1jqsKcgDfn7IrpKJfFEF8I5We8PefJqEnrP/lDKD/jzTnXARJR81tPodww9wFLhBAnpJQb/CGoD/H2Oo8H1qJu4gD5wBAp5X7fiucfpJSZHg4J6D1MKx/XmIx35zKv9nZX5WNNLvrb2ytUbjZAeHPORRgTtNOBR1CRX5/6Vjy/4PE5G5O3LwDDpJTn/Cibv/DmOldDKaA/SSm/ABBCfIN6Un4GZSFUZry5zm1R0W37UA8bF1Au1k+EELdKKTf6SdZgEtB7mHa7ucZ+U3HW9rFO253HuHo6iC2lf2XDm3MGiqLePgYeQymex30vnl/w6JyFEKGoieblqMCKMGNSFyDE4e/KjDfXOQewoCLFADBcrV+jXHKVHW/O2R6YcLOUcpWU8ivgTuA34HXfi1gpCOg9TCsf19h9w62c2ls5bXce08KwAJzHuOpf2fDmnBFC1EDdhO4EJlchxQOen3MToCcqBNXs8AJ4FjciiioB3lznvah7RbhTezVcPylXNrw556bALinlmaKdKIX7PZDkcwkrBwG9h2nl4wIp5T6UX9t5DcAwYK+UMsPFsK+AmkB/e4MxSXkDsM5PovoMb87ZsAQ+Ba4B7pJSzva7oD7Ei3M+CnR38QJ4x+HvSouXv+0UlOvlTnuDYeXdClR695OX5yyB9i7W9FyDWqB6ORLQe1hVcBMEi+eABUKIM6gFWoNR/3x3QdFFaYl6OsqWUn4nhEhFTcI+jgrLfAY4i7oxVQU8OmdU7H9fYB5wSAhxjcO+bFLKTQGU3Vs8PWfnsHLUNBBHpZQltlVSPP1trxdCrAbeMFbA7wEmAM2BPwfjBLzA0+v8GvAX1Hqgl1FzPqOBPvYxVZ1g38O05VMKUsoPUTfXW1ChlX2B0VLKpUaXQcBPQFeHYUOBz4BXUaG4h4F+jqZ7ZcaLcx5mvI8z2h1fPwRE6Ari5XWu0nh5zncAc1Gr/VehAhAGSCm3BkbqiuHpOUspD6AWmR5H/S8vQbldBziMqeoE9R5mstmqgstWo9FoNJcT2vLRaDQaTcDRykej0Wg0AUcrH41Go9EEHK18NBqNRhNwtPLRaDQaTcDRykej0Wg0AUcvMtUEFSHEM8C/yunWRUq5zYN9HgAOSCn7ei1YJcfhe2turEmxl3pIdPjcF5X086/GOpcqgRCiRVXJHK3xHq18NJWF/8el1PXOHAykIFWElaiMyyehKMfeOmA1alU6qO9zFCo7c5VACDEPuAq4MdiyaPyLVj6aysLXUsrUYAtRVTCKnf3PoakWKrfcaoc+mcC/AyxaRbmFyzd3msYBPeej0Wg0moCjLR9NlcFI9T4OGAu0RaX4PwAsAF5xLOftNC4eVYPlJqAeKl/VMuBZKWWeQ792wIsol081VO2W56SUa8uRKxVVpng2qqBecyANeEFK+YlT3w7A86jcYhHAduBlKeUqhz4Rxn4GA42AE6h8W0/ac2w5zvkAzbhU0O1fQgjn9r8C/0HlKdsopRzsJNM9qO+wj5FcMgRVz+Zvxn5OASuAp4ykm6V9D32N490DPIqqaPuxlHKsEKI+8CQw0DinPGCrsc8fjPH269fU+LtorsqQ8WHUdc8BvgSmSSmPlSaPpnKjLR9NZSFOCFHbxcuxhszzqOy6u4C/A0+gbmIvozIOl8Yy4DZgPvAgkIpKkPmGvYOhFH4C2qHmn/6JUm6rhRAj3JC/LeoG/S0wBVX5cYUQoijrsxCiO/AzqibQTEP+asB/hRAPOuzrLdSNfwkqe/QK4H6gtISWu7lU/Oy/qHmek44dpJT5wCfAzUKIuOLDGQEc4lJ5hPeBV1DJYR9CFc97AFgvhIgs53sAeNvY1+PAZ0KI6sbnO1HJKiegkpR2Q32/9qJuo1CKLs34+zsAQ5kuQM1xPQK8C/wf8JMQorYb8mgqIdry0VQWVpXSfiOQaiihScASKeU99o1CiPdQlsEwVJXRYggh6qLqkzwmpXzVaH7PsKJaOHR9E3XD7iqlzDXGvgmsB2YLIf4rpSwoQ/6GwCNSylnG2PmoOZkZQoglUkqrcQwr0F1Kedjo9w7qJj9DCLFUSnkKuBv4QEr5hMN5nAduFULESCnPOx5YSpkphFiFsu7+J6X8tzHGWcaPgHtRFtVio0+C8f3MlFLaDOvlHuABKeU8h+OvBtaiLM/y6jZtkVJOcBg7AlWQ7FZHK1IIsR+lhAYAK6WU/xZCvABkOpxDC+BplHU4zWHsf4BfUQ8JdsWrqUJo5aOpLDyKckE5sx1ASmkWQtSjZDXN2kA2EFPKfs8B54EJQoh0IEVKmSulHGvvYNyA+6CUQ3XjSd3Of1G1XbpTdpmIc8Ac+wcp5UVDscwErhZCZKAsnnfsisfolyeEmIFyiw0w3g8DI4QQW4BVUsqzUsqngKfKOL47fAscQVkgi422Yaj7wEcOn20oi8TRqvgV5ba7jfKVTzE3pZRyqRBiPcqqAUAIUc2hS2nXDpSFE4KyoBzlOY5yi96GVj5VEq18NJWFrW5EuxUAg4QQtwMCNadgrzTp0oUspcwXQoxDudxWAPlCiG9RLqhFxpxPS6P7JOPlikTKVj5/uLCM9hrvzRzkc1WO2B5i3tR4H49yFS4A5gshfkIpwQ+klOfKkKFMpJRWIcQSYJIQIs7Y1whgp5Ryh9GtJapqqavqnqAUfXmccNFmBaYKIa4zjtGKSw8SZbn/7demtHDxsqxRTSVGKx9NlcBwk/0bGAl8j7oZzUPNC6wva6yU8mMhRAowBFVAqz9wM8oa6gmEGl3fpnT33+/liOjqJmjfrwV1Qy8N+823wJD3GyFEIvAn1JP9zSjr6xEhxNVSypOud+MWHwH/AG4XQqxFWXxPOsmcgyoq5oqLbhzD4vhBCNEUNdcVjSrVvATYhvpOSvu+HeUB5Sp059iaKoJWPpqqQm+U4nleSvm0vVEIEQYkAC5XxBtlnzsDv0spPwA+MFw+r6Cip27mUmnsQinlOqfx7VARXxfKka+5EMLkFHHX2njfy6UAgDauxDTeDxmRbp2Bw1LKJaiSxiGoAIsZqBLOb5YjS6lIKX8TQuxGKeIYlOL7j0OXAxjfiZTybDEhhRgGnPbisP8C6gJtpJR2axDHYIwyOGC8H3LOciGEGIhyd2qqIDraTVNVSDDedzm1/w2IovQHqfaoSKt77Q2Ge+w346PFCNfdAtwjhGho72cEOXyActeV96BWDzWXYh8bhXKf7ZVS7pBSHjeO8RchRGOHftVQiiUf+Bq1WPQnoGhy3QhW+MUubynHt7e78z/9EWp+6U7geymlYwaJz4z3fzoOEEL8CfU9uKMwnEkAcnHIVGGc9wPGR8fv1kLxc/jceJ9mWL/28Z0NWSd7IY+mEqAtH01V4UfUfMPrhkvqLCoSbgQq3Dq2lHGbUMrnRWPc/4AmqLmdNFRKGlAhxeuBrUKIOagn/JGoIIFpUsrynvjNwAIhRFfgKGotUmOU28yO/Ri/GMfIAf4CXA08ZFgaZ4UQH6FcgtHGeScAE4FM1FyQK06j5lUGCyEOotLvlMbHwAsol9sDTttWA58CjxqRZl+j5qwmouaBXsVz1qDcZl8KIZYDccAYLs3nOF67k0AnIcR44Fsp5U4hxBuo7y7BiOqrhbp+OVQ8CEMTJLTlo6kSGKliBgJ/oG44/w81QX8XKsosyYiGcx5nQ7mY5qIUwVuoNTOfADfagwSklD8BvVDWyT9QLq5o4B4p5ctuiHgUZRUMM2Q7B/SXUn7lIIv9GFtR0X0voBTnECmloyvtftSaputQa5EeRQU7XG+EYrv6fi6grJUmKLdcp9IElVKmo5SaGbWGx3GbDRiOmgdqj4ps+wvq++ptXAdPmYda09TCOJ+JwE6gIyoC7iaHvv8CzgCzUJFuoKybCUAdlPJ7EPVAcb2UMs0LeTSVAJPN5nJRuEajcRMjw0EzKWWzIIui0VQZtOWj0Wg0moCjlY9Go9FoAo5WPhqNRqMJOHrOR6PRaDQBR1s+Go1Gowk4WvloNBqNJuBo5aPRaDSagKOVj0aj0WgCjlY+Go1Gowk4WvloNBqNJuD8fwfojnMrCbArAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu1 = 0\n",
    "sigma = 1\n",
    "n = 1000\n",
    "\n",
    "res = []\n",
    "for mu2 in [3, 2, 1.5, 0.75, 0.25]:\n",
    "    sample1 = np.random.normal(mu1, sigma, n)\n",
    "    sample2 = np.random.normal(mu2, sigma, n)\n",
    "    \n",
    "    d = (mu2-mu1) / sigma\n",
    "    label = 'd = %0.2g' % d\n",
    "    auc = plot_roc(sample1, sample2, label)\n",
    "    res.append((d, auc))\n",
    "    \n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This function computes AUC as a function of `d`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_auc_vs_d(res, label):\n",
    "    d, auc = np.transpose(res)\n",
    "    plt.plot(d, auc, label=label, alpha=0.8)\n",
    "    plt.xlabel('Cohen effect size')\n",
    "    plt.ylabel('Area under ROC')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The following figure shows AUC as a function of `d`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_auc_vs_d(res, '')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not suprisingly, AUC increases as `d` increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Multivariate distributions\n",
    "\n",
    "Now let's see what happens if we have more than one variable, with a difference in means along more than one dimension.\n",
    "\n",
    "First, I'll generate a 2-D sample with `d=1` along both dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 0], [0, 1]]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import multivariate_normal\n",
    "\n",
    "d = 1\n",
    "mu1 = [0, 0]\n",
    "mu2 = [d, d]\n",
    "\n",
    "rho = 0\n",
    "sigma = [[1, rho], [rho, 1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample1 = multivariate_normal(mu1, sigma).rvs(n)\n",
    "sample2 = multivariate_normal(mu2, sigma).rvs(n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The mean of `sample1` should be near 0 for both features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01204411, -0.05193738])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(sample1, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "And the mean of `sample2` should be near 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.97947675, 1.02358947])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(sample2, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The following scatterplot shows what this looks like in 2-D."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = sample1.transpose()\n",
    "plt.plot(x, y, '.', alpha=0.3)\n",
    "\n",
    "x, y = sample2.transpose()\n",
    "plt.plot(x, y, '.', alpha=0.3)\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Scatter plot for samples with d=1 in both dimensions');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Some points are clearly classifiable, but there is substantial overlap in the distributions.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can see the same thing if we estimate a 2-D density function and make a contour plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Based on an example at https://plot.ly/ipython-notebooks/2d-kernel-density-distributions/\n",
    "\n",
    "def kde_scipy(sample):\n",
    "    \"\"\"Use KDE to compute an array of densities.\n",
    "    \n",
    "    sample: sequence\n",
    "    \n",
    "    returns: tuple of matrixes, (X, Y, Z)\n",
    "    \"\"\"\n",
    "    x = np.linspace(-4, 4)\n",
    "    y = x\n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    positions = np.vstack([Y.ravel(), X.ravel()])\n",
    "\n",
    "    kde = gaussian_kde(sample.T)\n",
    "    kde(positions)\n",
    "    Z = np.reshape(kde(positions).T, X.shape)\n",
    "\n",
    "    return [X, Y, Z]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, Y, Z = kde_scipy(sample1) \n",
    "plt.contour(X, Y, Z, cmap=plt.cm.Blues, alpha=0.7)\n",
    "\n",
    "X, Y, Z = kde_scipy(sample2) \n",
    "plt.contour(X, Y, Z, cmap=plt.cm.Oranges, alpha=0.7)\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('KDE for samples with d=1 in both dimensions');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Classification with logistic regression\n",
    "\n",
    "To see how distinguishable the samples are, I'll use logistic regression.\n",
    "\n",
    "To get the data into the right shape, I'll make two DataFrames, label them, concatenate them, and then extract the labels and the features. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.012044</td>\n",
       "      <td>-0.051937</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.971861</td>\n",
       "      <td>0.976814</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3.580857</td>\n",
       "      <td>-3.061129</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.596927</td>\n",
       "      <td>-0.696824</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.071937</td>\n",
       "      <td>-0.044057</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.655457</td>\n",
       "      <td>0.615113</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.053507</td>\n",
       "      <td>3.292066</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0            1   label\n",
       "count  1000.000000  1000.000000  1000.0\n",
       "mean      0.012044    -0.051937     1.0\n",
       "std       0.971861     0.976814     0.0\n",
       "min      -3.580857    -3.061129     1.0\n",
       "25%      -0.596927    -0.696824     1.0\n",
       "50%       0.071937    -0.044057     1.0\n",
       "75%       0.655457     0.615113     1.0\n",
       "max       3.053507     3.292066     1.0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame(sample1)\n",
    "df1['label'] = 1\n",
    "df1.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.021376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.021376</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0  1.000000  0.021376\n",
       "1  0.021376  1.000000"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1[[0,1]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.979477</td>\n",
       "      <td>1.023589</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.983136</td>\n",
       "      <td>0.967058</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.231272</td>\n",
       "      <td>-2.027548</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.291482</td>\n",
       "      <td>0.417082</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.008545</td>\n",
       "      <td>1.008277</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.670930</td>\n",
       "      <td>1.647037</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.869119</td>\n",
       "      <td>4.138071</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0            1   label\n",
       "count  1000.000000  1000.000000  1000.0\n",
       "mean      0.979477     1.023589     2.0\n",
       "std       0.983136     0.967058     0.0\n",
       "min      -2.231272    -2.027548     2.0\n",
       "25%       0.291482     0.417082     2.0\n",
       "50%       1.008545     1.008277     2.0\n",
       "75%       1.670930     1.647037     2.0\n",
       "max       3.869119     4.138071     2.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.DataFrame(sample2)\n",
    "df2['label'] = 2\n",
    "df2.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>-0.04433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.04433</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         0        1\n",
       "0  1.00000 -0.04433\n",
       "1 -0.04433  1.00000"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2[[0,1]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2    1000\n",
       "1    1000\n",
       "Name: label, dtype: int64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.concat([df1, df2], ignore_index=True)\n",
    "df.label.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "`X` is the array of features; `y` is the vector of labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[[0, 1]]\n",
    "y = df.label;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we can fit the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "model = LogisticRegression(solver='lbfgs').fit(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "And compute the AUC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.853391"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_auc_score\n",
    "\n",
    "y_pred_prob = model.predict_proba(X)[:,1]\n",
    "auc = roc_auc_score(y, y_pred_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "With two features, we can do better than with just one.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### AUC as a function of rho\n",
    "\n",
    "The following function contains the code from the previous section, with `rho` as a parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def multivariate_normal_auc(d, rho=0):\n",
    "    \"\"\"Generate multivariate normal samples and classify them.\n",
    "    \n",
    "    d: Cohen's effect size along each dimension\n",
    "    num_dims: number of dimensions\n",
    "    \n",
    "    returns: AUC\n",
    "    \"\"\"\n",
    "    mu1 = [0, 0]\n",
    "    mu2 = [d, d]\n",
    "\n",
    "    sigma = [[1, rho], [rho, 1]]\n",
    "\n",
    "    # generate the samples\n",
    "    sample1 = multivariate_normal(mu1, sigma).rvs(n)\n",
    "    sample2 = multivariate_normal(mu2, sigma).rvs(n)\n",
    "\n",
    "    # label the samples and extract the features and labels\n",
    "    df1 = pd.DataFrame(sample1)\n",
    "    df1['label'] = 1\n",
    "\n",
    "    df2 = pd.DataFrame(sample2)\n",
    "    df2['label'] = 2\n",
    "\n",
    "    df = pd.concat([df1, df2], ignore_index=True)\n",
    "\n",
    "    X = df.drop(columns='label')\n",
    "    y = df.label\n",
    "    \n",
    "    # run the model\n",
    "    model = LogisticRegression(solver='lbfgs').fit(X, y)\n",
    "    y_pred_prob = model.predict_proba(X)[:,1]\n",
    "\n",
    "    # compute AUC\n",
    "    auc = roc_auc_score(y, y_pred_prob)\n",
    "    return auc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can sweep a range of values for `rho`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEtCAYAAABdz/SrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xd4lFX2wPHvpBECoYTeO4eOSESkKCp2RBEQy6qsdS2/xbLu6q5r38Wy1rVX7OAqKlYUBURA6R0OvXdCIBBISPn9cd/BYZiUCQmTcj7Pk2fI+973zpmQzJl731t8ubm5GGOMMaVNVKQDMMYYY0KxBGWMMaZUsgRljDGmVLIEZYwxplSyBGWMMaZUsgRljDGmVIqJdACm5IjIGcCPwC6goapmBp0fBVwDtFDVtSGu7wdMBB5S1QeDziUCNwKXA21wv0uLgTeAN1Q1p3hfzfElIncAfwVqAM+p6j0RiiMRiFfVHd73DwIPkMf/WaSJSH/gv0BLYIaq9o1wSEVyLD9nEYkCmvqvC/g7+qOqjirOOMs7a0GVb1cA+4FawMDiqlREBJgFjAQWAn8H7gcOAq8C74qIr7ie73gTkc7A08Ba4P+ATyIUR3dgGdAx4PBY4CpgRyRiyo/3xvwhLqnfATwZ2YiOPxGpBvwKDA84vBT3f/ZzJGIqy6wFVU6JSCVgMPAuLlENpxjeaEUkHvgCqA0kq+qCgNNPiciLwC3ADOD5Y32+COnsPf5bVb+McBwNAw94P+8FoYtHXH2gDvC0qr4U6WAiJAk4CfjGf0BVtwHvRyyiMsxaUOXX+bhPshOB8cC5IlK/GOq9BRDgjqDk5PcXYDfwp2J4rkiJ8x7TIhpF2WM/N1OsrAVVfl0J5OK6FaKBS3HdDMfa7XIZsA/4KNRJVT0gIicD6/KrxOsCvAm4FmgPxOK61N4GnlDVXK9cTeAZ4AygHrAR+Bh3X+xgAc8xBNdFdwJQGdgE/A/4p6pm5HHNJOA079uJIoKq+rzjzVW1eYjyh4973x8EngUeBToB24G3gIcD782JSDvgYe+1xQJzvdimBNwD8cexTlWbh7o3IiK1gEeAi3AtW//P8UlVzfbKPAjcg2uVPeO9xixgHHCnqu4q4GeZ73MExfuAiDwAnK6qk/KorxrwEK6VXxtYhbvX90ZhnzPodV0OvAxUAW4HmoQ6rqpver9TDwOXePWuBl4Bnvf/3uUR84nAP4A+uJbSbmAC8FdV3RhwrynwZ9ACaE7QPSgRiQbuBK73zu/C9Uz8U1V3emX89Z0NXAwMBaoC03H/Z/PzirW8sBZUOeT98V8ATPe6F74GMjiyX7wo9fqAbsBsVT2UVzlVXRE8ICOER3BvHEtwf6h/x72xPwZcHVDuY2AA8DpwKzAJ98aTb/ehiFyPS0apwN9wLbt1wN3e9Xn5F/Ca9+9/45J6uDp7cU8C/ox7A3yAgFaliLQBfsMlpxdwrz8J+EFETsLdawqM4/ZQT+S92U4DrsN14d6Bu+cxEnc/KFA07g0vDffz+BT3s345vxdTyOcY6x0H+Az3c1uaR31xuA9O/wd85V23GnhdRP5chNcVixuc8wzwH+CXvI6LSBXvua8C3sH9XBfhPlC8kM/PoLNXb2svhluBb3Ef2N7zii0N8TPI617haOAJ77nv8F7j9cBUEakRVPYN4ETc38zjQE/gGxEp9w2Mcv8CK6jBQDzuTQNVTRORCcAFInKSqs4sYr21cb8zW44lOBGJxb05jVbV4QHH38C1NgYD74hIXaA/cLeq/scr9oaXKFsW8DR34T5pXhzQGnsJWOPV/1Coi1T1BxFphBuh+ENeLYACNAQG+u9fici7wGZcq9Z/b+ZR3Btod1Vd6ZUbjWtJ3K2ql4rI9ELE8TegLTBIVT/3jr3kvxcoIqNU9VvveAwwRlXv8r5/1Xutg0QkQVXTj+U5RGQvLhksUNX87rlcB3QFrlTVD73X/howGbjXqzec1xUF/FdVH/c/gRvHE/L4g169yaq60Dv8soj823vu1/JomdyC65E4XVVTvGOvecn2MhFJUtVtIvJ58M/Ai+UwETkXGIJrMd4ecHwK7oPNvd7r99sG9AloNfo/yJ0O/BAi1nLDWlDl05Xe49iAY/5/Dy9Cff5uj2zvMboIdRzmtb7q4d58A9UG9uK6MQD24LoTbxGRwd6nX1T1WlXtX8DTdAHOD+qyqYvrlqka+pJik45rtQLgdUUqbhCBf7Tb+cA3/uTklduF6z76cxjPNRBYGvAm7veI93hx0PGPg76fh0tctYrxOQoyANeyONxN7P0/XQX0BXKK8Jzj83iu4OODca2WLSJS2/8F+J9nQB713ILryvUnJ39Phb+bOZzfKf+I2pGBB1X1f7jfk+DX9qk/OXnmeY/FcU+5VLMWVDkjIg2AfsByIFdEmnun5uMSzeUicqd3D8b/x5XX74H/uL/cbiAT90Z/rDJxLbqLcIMu2gA1vXNRAKqaISI34br3PgEyRGQyrmvq3fzuQanqIRFJFpHLgXa4rhl/3PneHysGu0LMA8vg98ReC/eGtiL4QlVdFOZztQC+C1HPVhFJBZoFnQrucvLfi8vvQ0e4z1GQ5sCq4Ps9qnr4/0VEwn3O7Xk8V/DxVrj7kXl1vTUNdVBVc0Wklojci/vw08qLwT+dIpwP+y2AVK/7PdhS4LygY0X5PysXrAVV/lyG+8Vti+vO8n/Nwv0x1cTddAaXcAAS86jLnzBS4fCn3OlA9/z6v0XkURH5KK9Rg14X3fu4pNMCd6/hL7gktSGwrNcF1ATXLfQ1rv/9VeBXbyh9XjGMxHV/dMN94nwA1600Ja9riijUm0RBk5T91xTHZOb85ptF4T4IBCrKc4b7HAWJLkQc4T5ndqiCIY5H4+4lnZXH13OhKhGRC3AtryG4gTov4LrYRoYqX4Dj8X9WLlgLqvy5AtdSuoajh/t2BR7EdfN9jBugAG4i6NwQdfnnAwV+qh+LGwE2DPgg+AIRqYy72RuNG5kUSl/c6KpHVPX+gGv9XU2rve+r4kbgLVbVt4C3vD7/J4ARuNFNR81TEpFmuIEQ76nq1UHnitotkg2ESohFqW8ncADXqjuCiPwFqK+qfylkXWtxLcTgeuoD1QhK+EVU3M+xHtcKCa7vPNwHrL+WwHP6rQUSVXVCUL01gTMJ0ar1/Nc7l6yq+wOuuzKP8gXFcI6I1AvRihKK5/+sXLAWVDnijQxLBiap6nuq+nngF2402FbgbBFpiGthHABGeIklsK4auES2AQgcVPEarovsKRHpFHRNNG5EWD3g8XxG+vnvdywJOn4DkMDvH5w64Vo81/kLeKMD/ck0r0/NSaHqF5Hz+X1ZpnBtBep6Pzd/fd0JkWQKoqpZwPfA+SLSJKC+mrhRhq28Q/7Xl9/f6ZdAOxEJvm/hH6n4VbjxHYfn+AaoJyKDgo7fgRt9urMEntNvHNDVaxEFug836rPT0ZcA7nd2XVByaoIbqg6//04V9v8M3GCIw7zXKhTP/1m5YC2o8sX/ae7NUCe9+zJv4YY0X6Wqj4vI3bhPh7O90WbbcP3ww3GrAgwKHDKuqge9N5bvgZki8gEugdXCzdM4AfeH/nQ+cU7DDYZ4RkSa4roQT8e1yg7ye5fjb7gE9S+v3AJcd9//4ZYAmkBoS3Cf0v8ubuWLjUAP7zUF1h+Oj3Ct029FxJ+E/w/3qTouvwvzcC/u9c0QkRdwP48bcPem7vPK+O893Cwi9f0j3oKMxN34H+PFtRzXErgEGBsw0u1YFPdzvIqb/zbaG5WnuMR0FnCtN6+qpF6Xv96xIvIKbv3IPrgBGt96X6F8CwzzrpmJG0V6A25+Ffz+O7ULb5CHiKzjyIFKft/g5jyNEJHGwE+4Lvmbcb0HRek2LJesBVW+XIEb+Rbqj8LvNdwf0HAAVX0ROBf3hzECN2HxOtx6Yqeoaqgb1XNxiegF4BTcHJN/4N78rwWGhRgkEHj9NtwotlXAP3Etu2a47p2XgI5e90cubkTTK7jRVS/gRv59ihvuG/LehzcA5Hzc/bIRXnzdvX//DajmtX4KTVW/ws19qYy7TzEE94byfTj1BNS3FPezm4Hr0noYN3y/j6ou9or9iOuKvQB4wUu2wfWkePW8i/v5PY2b+Hw3bnL2MSvu51DVA7iBPG/iunqfARoBl6rq2yXxnCFeyyjcB6rncfc1HwGG5PN7e7MX70W4D3RDvNjO9M6f4dWfjvtbaOKV6xoihlzvuf/pnX8GlzRfA05S1dSivr7yxpebm+fEaWOMMSZirAVljDGmVLIEZYwxplSyBGWMMaZUsgRljDGmVLJh5oUgIlm4ZL430rEYY0wZUQ3IUdUi5xlLUIUTBfgSExOrRzoQY4wpC9LS0uAYe+ksQRXO3sTExOqzZs2KdBzGGFMmJCcnk5aWdky9TnYPyhhjTKlUalpQInICbgmRFqq6MZ9yVXG7Sg7GLQvzMzBCVVcElInBrV49HLcEz2zgLlWdUWIvwBhjTLEqFS0ocVtOfkXhEuYY3DIhf8NtV90ImCgigfeHnsNtI/44bn23LGCCiBS0C6sxxphSIqItKK+lcyNu++K8Vr4OLN8Ht8baef414rxtktcAfwIe9zbouwm4TVVf8cp8j1ts8m7cmlrGGGNKuUi3oPrg9vZ5CtciKsjZuD2OfvAfUNUdwGRc4gK3aGM0bkFRf5kMXAvtfIwxxpQJkU5QS4GWqvoQrhuuIO2AlaoavA/QStw+Kv4yu73EFVymafC+R8YYY0qniHbxhdhNsiDVCT1ZNg03KaygMuD2bTkQ5vMW2cy1KVSLj0XqF2ULImOMqbhKzSi+QvLhtjMPdTynEGUIKFfiFmxMZegr0wHo0SKJ4b2ac3aHesRER7rhaowxpV9ZS1B7cDtZBkv0zvnLVMujDBzH5Yqa1EygU6NqLNq0lxlrUpixJoUG1eP5Q89mXN6jKUlVirIRqzHGVAxl7aO8Ai1FxBd0vLV3zl8mSURqhiizJq9dWEtCzSpxfHlbH967rgf929fF54Mtew7y5Hil58gfuefTBWzbe/B4hWOMMWVKWUtQ3wM1gP7+AyJSBzgVmOAd8o/wGxJQphJu22x/mePG5/PRt00d3rjmJCb/5XSu79OCxPgYMrNyGD1zA/2enMRzE1ZwIDN43IcxxlRspTpBiUgdEekpItUAVPVnYBIwWkSuE5FBuKSTCrzslVkHvAM8LyJ3iMgA4FugJm5Ie8Q0rZXAfQM68Ou9Z/LQwI7UqhLHgUPZPDNhOWc8NYnP5m4kJyfU7TNjjKl4SnWCwrV6pgMnBhy7BBgH/AcYBWwEzlTV3QFlbgJeAe7BrTwRA5ylqiuPQ8wFqlIphmt6NWfi3f246bSWxEVHsWXPQe4YM59BL01l1tqUSIdojDER58vNtU/sBRGR1JJczXxDSjqPfbuMrxduOXzshr4tuPucdsTFlPbPEMYYczRvNfM9qlqjqHXYu18p0CQpgRevPJH//ekUOjdySwq+PmUNQ1+dzvpd6RGOzhhjIsMSVClyUvMkPrulF7ed3hqfD+ZvSOWC56fw9YItBV9sjDHljCWoUiYmOoq/nCO8d+3J1K5aibSMLG79cA7/+GwhBw/ZSD9jTMVhCaqU6tOmNt+O6EvfNrUB+OC39Vz84lRW79gX4ciMMeb4sARVitVJrMQ7f+zB3ecI0VE+lm1N46IXpzJx2fZIh2aMMSXOElQpFxXl49bTWzPmxp7USaxE2sEsrn1nJi9NWomNwDTGlGeWoMqI5OZJfHlbH7o2qUFuLjzxnfJ/H821FSiMMeWWJagypH71eMbc2JMh3RsD8NWCLQx+eRobd9tQdGNM+WMJqoyJj43mySFdeODCDkRH+ViyZS8DX5jKnPW7C77YGGPKEEtQZZDP5+OPvVvw3rU9qJkQS8r+TO4cM49sW8fPGFOOWIIqw3q1rs2HN/QEYO2udH5YsjXCERljTPGxBFXGtW9QjTPb1QXgtZ9XRzgaY4wpPpagyoEbT3WbDM9Zn8rsdbYSujGmfLAEVQ70aJFE18ZukdlXJ1sryhhTPliCKgd8Ph83ntoKgB+WbrPlkIwx5YIlqHLinI71aJJUmdxceOOXNZEOxxhjjpklqHIiJjqK6/u4e1Gfzt7Izn0ZEY7IGGOOjSWocmRocmOqV44lIyuHd6evi3Q4xhhzTCxBlSMJcTFc1bMZAO9NX2vr9BljyjRLUOXMNb2aExcdxe70Q3wye0OkwzHGmCKzBFXO1EmsxCUnNgLcYAlb/sgYU1ZZgiqHru/rBkuss+WPjDFlmCWocqh13ar0b++WP3r6h+VsTj0Q4YiMMSZ8lqDKqZv7tcbng+Xb9nHOsz/z+dxNtgOvMaZMsQRVTnVvVpPXr0qmVpU40g5mcfuYedz20VxS0zMjHZoxxhSKJahyrH+Heoy/41T6t68HwNcLtnD2Mz8zefmOCEdmjDEFswRVztWuWonXr+7OE4O7UCUumu1pGVzz1gwe+GIRmVk5kQ7PGGPydEwJSkTiiisQU3J8Ph+XntSEb0ecyknNawLwzvR1XPXmb+zeb11+xpjSqcAEJSIDROQrEfGFOP2yiMwVkUElEJspZk1rJTD6xlO4o39bAH5bk8Kgl6ayylY/N8aUQvkmKBF5FBgHnA20yaNYB+ATEXmymGMzJSA6yseI/m148YoTqRQTxdpd6Qx6cSrTVu6MdGjGGHMEX15Dj0VkCPAx8BVws6puyqNcPeA94EzgIlX9KpwARORy4D6gJbAWGKmq7+ZTvgvwBNAXOAB8A9yjqpsDyvQBpoS4/GtVHRBOfF59qYmJidVnzZoV7qWl2rwNqVz/zix27ssgJsrHIxd34vIeTSMdljGmHEhOTiYtLW2PqtYoah35taBuA+bjkk7I5ASgqtuAC4E1wIhwnlxEhgIfAN8DFwOTgHe85BiqfCtc4mkJ3AhcDTQApolI4A+hK7AfOCXo665w4ivvTmhSgy9u6027+olk5eRy79iFPPrVElseyRhTKsTkc64b8KiqFvhupaoZIvIecEeYzz8S+FhV/deNF5Ek4BHgkxDlRwCxQH9VXQ8gIj8BCvwV+LtXriuwSFV/DTOeCqdRjcp8cnMvRnw0lx+XbeeNX9awcsc+nrusG9Urx0Y6PGNMBZZfCyoK2BNGXZvJP+EdQURaAq2AT4NOfQK0E5EWoS4DFvqTE4CqHgRmAOcHlDsBWFDYWCq6qpVieO3qZK7v437kk3QHF784lZXb0yIcmTGmIssvQa0BOodRV0cgnP0d2nmPGnR8pfcoIa5ZDzQSkeBE2NL7QkSigE5AYxGZIyKZIrJeRO7KYySiwQ2euG9AB54a2pW4mCjW7NzPxS9OY8KSbZEOzRhTQeWXoMYC14hIw4IqEZFGwHBgYhjPXd173Bt03P+xvVqIa94FGgJvikhTEakrIv/CJccqXpm2QGVcgnscOBf4DHgSeDCM+Cqkwd0b87+bTqF+tXj2ZWRxw3uzeOGnFbaOnzHmuMsvQb2IG2gwWUR651VIRHoBPwDRwNNhPLe/NRP8zuc/ftQyB6o6BbgWGAisA7biWmIvA+lesU3AeUBvVR2jqj+p6gjgTeBvIpIYRowVUtcmNRj3f73p3qwmubnwn++Xc+uHc0jPzIp0aMaYCiTPe0aqukNELgG+AH4WEQV+BbbgklFdoCeupZIGXKKqK/OqLwT//a3gllJi0PnguEZ5AzJaAXtUdZuIvAWkeOfTgO9CXPo1cL0Xb/kaL14C6ibG8+ENJ/PAF4sZPXMD3yzcSlKVOB69OJxeX2OMKbp8BzWo6nQR6QDcDwzBdeMFWgs8CzymquGuQOq/99QaWBhwvHXQ+cNEpD3QXVXfB5YHnDoRmOOV6Qz0Ad5Q1UMBZSp7jzYjtZAqxUQz8pLO1K0Wz/M/ruDjWRsZcWZb6iRWinRoxpgKoMCljlR1p6r+GWgENAV6AN2BRqraUlXvKkJywmttrcElvkCDgRWBI/UCdAbe80YAAiAi/XDDyj/3DrUBXsJ18wUa5j3funBjrch8Ph9/Oq0lNRJiyczK4b3payMdkjGmgij0sHBvPtRGEdkH+FR1dzE8/8PA2yKyG7dixUDgUuAyABGpg+vKW6Kqe3HddGuAj0TkAVw34zPAb7gJv3j1zAJeF5G6uJGFV3p1Dy7MvC5zpIS4GK7u2Yznf1rJu7+u40/9WpEQV+hfHWOMKZJCrWYuIleJyHgRSQd2ATtFJF1EJojINUUdvq2qo4A/AefgWkD9gKtVdYxX5AJgOq4LD1XdjxuVlwKMAR4DRgPnqmqWVyYT13r6HHgAdw+tAzBIVT8rSpwGrjqlOXExUaSmH+KT2RsjHY4xpgLIcy0+OLzO3qe4ZYKycC2TzcAh3HDv7kACLokMVdUtJR1wJJTXtfjCde/YhXw0Yz1NkxKY+Jd+REfZtDJjTGgluhafiFTCrWR+Im6QRG1V7a2qQ1X1ClXth+tiuwu3LNLntj9U+XZ93xb4fLA+JZ3xi7dGOhxjTDmXXxffNUAyrmX0L2/49hFU9YCqPotb6DWZo0f5mXKkVZ2qh7ePf/Xn1flO3j2QmU1Wtu3Ya4wpuoIS1Feq+nVBlajqD7iVJ64ursBM6XTjqW4A5fwNqcxYkxKyzE/LttHjXxM4//kplqSMMUWWX4IS4Mcw6vqJ39fXM+VUcrOadGvqupRfn7L6qPPv/7qO69+ZRVpGFsu37WPqql3HO0RjTDmRX4KKx20IWFhZuBUmTDnm8/m4sa9rRU1Yuv3wiuc5ObmM/HYp932+iMDtpMbN2xyqGmOMKVB+CWol0CuMuk7h95XITTl2dsf6NKuVAMAbU9Zw8FA2fx49l1cnuxbVme3qcs95rjH9/eKtHDyUHbFYjTFlV34J6nPgchHpVFAlInICcAXwUXEFZkqv6Cjf4b2jxs7ZxBWv/8pXC9wMgz/0bMqrV3VnSPfGREf5SMvIYpJuj2S4xpgyKr8E9RSwA7fLbf+8ConIANzirOuAV4s3PFNaDenehJoJsWRm5zBnfSoA957Xjkcu6kRMdBS1q1aiV6taAHw5v1xOjzPGlLD8VjNPE5FzgW9wSWolbkLuFtz9pnpAX9z+S2uB872VHkwFUDkumqtPac5zP64gLiaKpy/tyoAuR24dNrBrQ6as2MmEpdvYl5FF1Uq2PJIxpvAKWs18sYh0Af4KXMXRw8jXAI/iVjMPZ0CFKQduOb0VifEx9GxZi06Nqh91/pxO9fnH54vIyMrhhyVbGdStcQSiNMaUVQV+pFXVPcA/gH94O+c2wG0quFlVN5VwfKYUqxQTzfV9W+Z5vlp8LKdLHcYv3sa4eZstQRljwhJWn4uXkPJMSiLyB2+vJmMAGNi1EeMXb2PKip3s3p9JzSq2GpYxpnDyTVAiEoNbxqgnrtU0BxitqtlB5ZrhBkicBViCMoed2b4uVeKi2Z+ZzTeLtnDlyc0iHZIxpozIb7HYusBM3LYWdwJ3AO8C80SkZkC5EcAi4GxgaolGa8qc+Nhozu5YH7BJu8aY8OQ3zPzfuJ1qX8G1oDoDfwOaA/8VkTgR+Qx4GsgEblTVU0s2XFMWDezqRvfNWJvC1j0HQ5Y5lJ3D2p02CNQY87v8uvj6A2NV9daAY4u9TQsfB14GLsJtCHiTqs3GNKH1bl2bGgmxpKYf4qsFm48aWLF2535ufG8Wy7ft46UrT+T8zg0iFKkxpjTJrwVVF5gQ4vh3QBXckPM/q+ogS04mP3ExUZzXySWdL+cf2c03Ubcz8IVfWL5tHwBv/bLmuMdnjCmdClosdm+I43u8xxdV9YXiD8mUR/5uvvkb97B2535yc3N5ceJKrh01k70Hf5/EO2vdblZu3xfJUI0xpUR+Caog3xZbFKbc69EiiXrVKgEwZtYGbv1wDk+OV3Jz4YQmNfjhzlNpklQZgP/N2hDJUI0xpcSxJKhDxRaFKfeio3yHl0J6edIqvlnotoy/NLkxY27qSYPqlRnavQkAn87ZyCHb6NCYCq+gibq1RKRp0LEk77FuiHOo6vpiicyUOwO7NuRN7x5TTJSPBy7swB96NsPn8wEwpHtjnpmwnJ37Mvlp2XbO8YanG2MqpoIS1LPeVygfhDiWW4g6TQXVpXF1+revi25L46mhJ9CjRdIR5xvWqMypbeowefkOPp65wRKUMRVcfsnkneMWhakQfD4fb1xzErm5uYdbTcGGndSEyct3MFG3s23vQepViz/OURpjSov8ttv44/EMxFQceSUngP7t65FUJY6U/Zl8Mnsjt57e+jhGZowpTY5lkIQxxS4uJopB3RoBbjRfbm5uhCMyxkSKJShT6gw7yY3mW7srnd/WpEQ4GmNMpFiCMqVO23qJnNCkBgAfzww9J2rvwUO8MnkVc9bvPp6hGWOOI0tQplTyt6K+WbSFvQePnHI3c20K5z07hce+XcaN786yOVPGlFOFTlAiUqskAzEm0IAuDagcG83BQzmHt+k4lJ3DU98rw16dzqbUAwDs3JfJJN0RyVCNMSUknDlLc0XkdVV9pDgDEJHLgfuAlsBaYKSqvptP+S7AE0Bf4ADwDXCPqm4OKBMDPAAMB2oBs4G7VHVGccZuSk5ifCwXdGnAJ7M38vGsDfRuXZvbx8xj/oZUADo0qEZMtI8FG/fw6eyNnNWhXoQjNsYUt3C6+OoAW4vzyUVkKG7C7/e4nXsnAe+IyJA8yrcCpuCS2Y24FdUbANNEpEZA0edwmyw+DgwDsoAJInLkPg+mVPN38y3YuIfznvuZ+RtS8fngplNb8tmtvbi2dwsAfly2jZT9mZEM1RhTAsJJUB8AN4pI82J8/pHAx6p6h6qOV9WbgY+BvFppI4BYoL+qfqCq3wAX4raj/yuAF99NuBbTC6r6JXAusBu4uxhjNyUsuVlNWtapAsDBQznUrxbPB9edzL3nt6dSTDTndKxP1UoxHMrOZdy8TRGO1hhT3MJJUDlAO2CFiCwVkcki8lPQ14+FrcxrzbQCPg069QnQTkRahLoMWBi43p+qHgRmAOd7h84AogPrVdUM4KuAMqYM8Pl83HxaK6J8cEHnBnx3e196ta59+HzluGgGdHH7TH06xxKUMeVNOPegzgJ2ev8uNI4iAAAgAElEQVSOB45aKDZM7bxHDTq+0nsUIHj3uvVARxGJUdWsgOMtvS9/vbtVj7pzvhJoKiKVVfXAsYVujpehyU24sGtD4mOjQ54f3L0xo2duYOGmPSzbupd29asd5wiNMSWl0AlKVUO1aI5Fde8xeFPENO8x1DvNu8B1wJsi8k/gIK7bryOu689fb6iNFv31JuIGV5gyIq/kBK4bsFmtBNbtSufT2Rv5xwUdjmNkxpiSVKR5UCLSUEROFpHqIhInIkWpx78gW/BaNv7jR01uUdUpwLXAQGAdbtBGO+BlID3g+lDr4+RZrym7fD4fQ05sDMBnczeTZXOijCk3wkosItJbRGYDG4BpQHegH7BeRC4N87n9W8cHt5QSg84fQVVHAbVxXYANVHUwrtWUEnBdqNaXv95QrStThg060a3dt3NfBj+vsDlRxpQX4UzUPQmYgHujD9wjKgW3u+6HInJeGM/tv/cUvFx166DzgTG0F5E/qGq2qi5X1W3eqROBOQHXJYlIzRD1rlFVG49czjSumUCvVm4e+SezN0Y4GmNMcQmnBfUobtBCV9zwcB+Aqs7yji0F/l7YylR1pVdf8JynwcCKPHbm7Qy8FzifSUT6ec//uXfoB+9xSECZSsAFuARryqEh3V0334Ql20lNt88gxpQH4SSoU4C3vRFwR9zjUdW9wGtApzCf/2HgChF5QUTOFZGXgEuBfwKISB0R6Ski/i67r3FJ7SOv/NW44eS/4e3wq6rrcJstPi8id4jIAOBboCZuBQpTDp3bqT5V4qLJzM7hy/mbQ5bZuucgy7elhTxnjCl9wh3ckJHPufhw6/PuJ/0JOAfXAuoHXK2qY7wiFwDTcV14qOp+3KTbFGAM8BgwGjg3aNj5TcArwD1euRjgLK/VZsqhhLgYzu/s5kQFd/Ol7M/kwXGL6fvET5z77M9MW7UzVBXGmFImnHlQvwFXAM8HnxCRKsD1wMxwA1DVV4FX8zg3ChgVdGw5kO+9Lm9i7h3el6kghnRvzP9mb2T+xj2s2JZG45oJvDV1Da9MWkVaxu+fX16etIperWrnU5MxpjQIJ0HdD0wSkcnAF7huvpNFpBPwZ6AZrjVkTESc1DyJJkmV2ZBygAfGLWbVjn1s2+sa/dXiYzinY33+N3sjU1bsZMnmvXRoaJN6jSnNCt0lp6rTgQFAY+A/uEES/8KN6KsMDFPViSURpDGFERXlY7A3J2raql1s25tBXEwUN57akp//ejqPD+5Cm7pVAXhjyupIhmqMKYRw7xn9gBuufRJulfArgF5AM1UdW/zhGROeId0bUyUuGp8PLunWiJ/uOo2/n9+eGglxREX5uKGvGwA6bv5mNqfagiLGlGbhdPEBoKq5uP2VZhd/OMYcm8Y1E/ju9lMBaJKUcNT5i7o15Inxys59GYyatpa/n9/+eIdojCmkPBOUiPxUhPpyVfXMY4jHmGMWKjH5VYqJ5o+9m/PkeOXD39Zz2xmtqRYfm2d5Y0zk5NfF1xJoEfTVEzcUvCuQAFTFzX3qh5tEa3/pptS78uSmVI6NZl9GFmNmbIh0OMaYPOTZglLV5oHfeys2fIXbRv19Vc0JOHc58AbwYkkEaUxxqpEQx7CTmjBq2lremrqG4b2bExtdpHWTjTElKJy/yueBN1T13cDkBKCqH+GS08PFGZwxJeXa3i2I8sGWPQf5esGWSIdjjAkhnATVGliRz/mNQKNjC8eY46NprQTO6+RWnnjt59Xk5obaocUYE0nhJCgFLhORo3aPE5F43D5NC4orMGNK2vV93R6cS7bsZdqqXRGOxhgTLJxh5o8BHwG/iMjbwGrc+nttgZtxK0lcUOwRGlNCujWtSY/mScxYm8JrP6+md2tb/siY0iSclSTG4FpJLXALsY7HLXn0HyAaGORN5DWmzLjhVDdxd/LyHSzdYntZGlOaFGX18YbAybiVJC4FuqtqS1X9uvjDM6ZkndmuLi3rVAHg1g/nsGtffgv2G2OOp6KsJJGDW7U87JXLjSltoqJ8jBzUmavemsHqHfv546iZfHhDT6pWCvtPwxhTzML6KxSRc4Ergfq4br1gtpKEKXNOblmL/17ejZvfn82CjXu48d1ZvDX8JOJjQ/2KG2OOl0J38YnILbgdba8AOnL0KhMtcKtPGFPmnNOxPo8N7gK4ldBHjJ5LVnZOAVcZY0pSOC2o24H5wHmquq2E4jEmYi5NbsKe9EP865uljF+8jb9/tpDHB3fB5/NFOjRjKqRwBkk0AV615GTKsxtObcnN/VoB8PGsjTz23bIIR2RMxRVOC2oVUK+kAjGmtPjrOUJqeiYfzdjAq5NXs25nOoNObMRpbevYfSljjqNwEtRI4DkR+VRVF5dUQMZEms/n49GLO7PnwCG+WbiV7xa7r8RKMZzdsT4DujagT+vatsCsMSUsnATVB9gHzBcRBXYAwXeRbRSfKReio3w8f1k3TpdNjJu/mWmrdpGWkcWnczby6ZyN1EyI5dS2dUhuVpPuzZKQ+olER9m9KmOKUzgJ6lwgF9iA2wuqWYlEZEwpERMdxdDkJgxNbsLOfRl8u2grX87fzMy1KexOP8QX8zbzxbzNAFStFEO3pjXo3qwmZ7SrS5fGNSIcvTFln89WcS6YiKQmJiZWnzVrVqRDMaXAlj0HGL9oKzPWpjBr7W62px29+sTwXs2557x2ds/KVFjJycmkpaXtUdUif1qz6fLGhKlB9coM792C4b1bkJuby8bdB5i9bjez1qUwbeUuVu/cz6hpa5myYgfPDutG58bVIx2yMWVSoROUiPxUmHKqekbRwzGmbPH5fDRJSqBJUgIXd2tEVnYOr0xexbMTVrBqx34GvTSVEWe24eZ+rYixQRXGhCWcv5iWHL1yRGugJ9APaI4bRGFMhRUTHcVtZ7Ths1t607puVbJycnnqh+UMfXU6a3buj3R4xpQphW5BqWrzUMe9DQwvAt7Abb1hTIXXuXF1vvq/Pjz+3TLenrqWuetTueD5KYz6Yw96tEiKdHjGlAnH3OegqtmqOhZ4HXj82EMypnyIj43mgQs78v51J1O/Wjzpmdnc+N4s1lpLyphCKc5O8RVA12Ksz5hyoU+b2nx80ykkVYkjNf0Q146ayZ70Q5EOy5hSr1gSlIhUAv4AbC+O+owpb5rWSuC1q7oTFx3F6p37ufmD2Ryy1dKNyVdxjOKrBAhQE3gg3ABE5HLgPtwgjLXASFV9N5/ydYAngHOAeGAacIeqrggo0weYEuLyr1V1QLgxGlMckpsn8eTQLowYPY9pq3bxz88XMfKSzrZaujF5CGceVEvcShLBsoFlwEfAS+E8uYgMBT4AngO+Ay4G3hGRdFX9JER5H/AZbvTgX4FdwEPARBHprKq7vaJdgf1A/6AqdmNMBF10QiNW79jPcz+uYPTMDbSsU4UbT20V6bCMKZWOeRTfMRoJfKyqd3jfjxeRJOAR4KgEBbQBegPX+FtZIrIUt9L6QOAdr1xXYJGq/loCMRtzTG7v34Y1O/czbv5mRn67jGa1qnBOx/qRDsuYUidiMwdFpCXQCvg06NQnQDsRaRHisnjvMS3gWIr3WCvg2AnAguKI05ji5vP5eGJIF05sWoPcXLh99DwWb94T6bCMKXUiObW9nfeoQcdXeo8SfIGqLgAmAveLSDvvftTzuAnCnwOISBTQCWgsInNEJFNE1ovIXV4XoTERFx8bzWtXJ9O4ZmUOHMrmka+WRDokY0qdSCYo/wJle4OO+1tH1fK47mbcgIyluFGDlwJDVXW1d74tUBmX4B7HrcL+GfAk8GBxBG5McahdtRIjL+kMwK+rU/h19a4IR2RM6RLJBOVvzQQPvPAfP2oMroi0B37F7UU1CDeS70vgUxHp6xXbBJwH9FbVMar6k6qOAN4E/iYiicX7Mowpuj6ta3NiU7fY83MTVhRQ2piKJZIJyt/pHtxSSgw6H8g/mOJsVf1cVb/HtaDmAs8AqGqaqn6nqluDrv2a34fEG1Mq+Hw+bu/fFoDpq3fxWyFaURlZ2aTszyQ1PZM9Bw6RdvAQ+zOyOJCZTU6ObZ9jyo9i3W5DROqo6o5CFvffe2oNLAw43jrofKBmwJKA4eSoaq6I/AKM8GLojNv99w1VDZyuX9l73FnI+Iw5Lvq2qU23pjWYuz6V535cwYcta+VZdumWvVz22q/sORB6JYq6iZW486y2DE1uYjv8mjIvrAQlIlcBg4GqHNn6isG1fDoCcYWpS1VXisgaYAjuHpHfYGCFqq4PdRlwjYjUDExSuBXV13r/boObj7UJGBdQZhiwBlhXmPiMOV78rahr3prBtFW7mLEmJeSCsqnpmdz03uw8kxPA9rQM7hm7kHenr+OBCztwcj7JzpjSLpyVJP6Km7eUiRvYUBvYiBvenQAcwI2oC8fDwNsishv4CjeX6VLgMu856+CGoi9R1b3A07gllcaLyGNAOnA1cJr/Gq+eWcDrIlIXt0X9lV7dg1XV+kBMqXNqm9qc0KQG8zak8tyPy/ng+p5HnM/OyWXE6HmsT0mnUkwUr17VnXrV4snJzSUnB3JyczmUncOHv61n7NxNLNmyl2Gv/cr5netz73ntaZKUEKFXZkzRhXMP6o/AfKAucApuMMPpuNF4t+LmKIU1MVZVRwF/wg12+By3r9TVqjrGK3IBMB040Su/FjdRdyswChgNNAHO8l+jqpm4QRKf45Ze+gLoAAxS1cCWmjGlhmtFtQFg6spdzFybcsT5ZycsZ/Jy13v+2ODO9JO6tG9QjY4Nq9O5cXW6NqlBcvMknh52Ap/d0otu3sCLbxZu5cynJ/Pk+GW29p8pc3y5uYVrUIjIAeBeVX3W+34XcKeqvuN9/yHQVFX7lFSwkSIiqYmJidVnzZoV6VBMOZabm8vFL01j/oZU+rSuzfvXnwzA+MVbuem92QAM79WcBwd2LLCunJxcxs3fzGPfLmPr3oMAXNWzGY9c3KnkXoAxAZKTk0lLS9ujqjWKWkc4LahDHLmCwwqgS8D3E3FzkIwxReDz+bj9TNeK+mXlTmavS2Hl9n3c9fF8AHo0T+IfF7QvVF1RUT4u7taIn/5yGlef0gyA935dx7j5m0smeGNKQDgJainQK+B7BZIDvq+BG8ZtjCmiflKHro3dHPYnvlNuem8W+zKyqFetEi9c2Y3Y6PBmhiTExfDghR05tW0dAO75dAErt+8r9riNKQnh/La/DfxRRN4XkSq4EXJ9ReQBEbkUN0dpfkkEaUxF4fP5GOHdi/ptTQqrduwnNtrHy3/oTt3E+AKuDi0qysezw06gQXW3q+8tH8zmQGZ2cYZtTIkodIJS1VeAfwMDcN19Y3GDFB7wHhOAv5VAjMZUKKdLXbo0rn74+wcHduTEpjWPqc6kKnG8cEU3YqJ8LN+2j/s+X0Rh7z8bEylh9Reo6n1AbVXNVNVcVb0CN8T7EqCtqk4viSCNqUh8Ph//HNCBGgmx3NC3BVf0aFos9XZvlsQ957k1mj+ds5GPZ20olnqNKSlhryShqlki0hA3vHsZ8BuQpao2htWYYnJS8yTm3X92sdd7XZ8WzFybwvjF27j/i8V0blSDDg3zWpfZmMgKqwUlIr1FZDZu8us0oDtu7tJ67z6UMaYUc3tRdaVpUgIZWTnc8sFs0g7mvTKFMZFU6AQlIicBE3BLGj0bcCoFd0/qQxE5r3jDM8YUt+qVY3npyhOJi4li7a50nvgu1LKXhbcn/RDv/7qOt6euIdsWqzXFKJwW1KO4tey64pY88gGo6izv2FLg78UdoDGm+HVqVJ27znLTFj+etYFd+zLCuj43N5ffVu/ijjHz6PHvCdz3+SIe+nIJb09dUxLhmgoqnAR1CvC2qh4gaA8nb52813A72RpjyoA/9GxGtfgYMrJyeP/XUGszH23Xvgxe+3kVZz49mWGv/cpnczeRkZWDz1s4/anvl7MhJb3AenakZfDfH1cUqqypuMLdDyq/j1nxRajPGBMhVSrFcGVPt8rEu9PXcvBQ/nOjNqSkc9YzP/Pvb5axesd+ALo2rs7ISzoz7Z4zqJtYiQOHsrn/i/yHsB88lM3wt2fw1A/LuXfswjzLGRNOQvkNuCLUCW/i7vXAzOIIyhhzfAzv1ZzYaB+79mfy2dxN+ZZ99OslpOzPpEpcNFef0oxv/tyXL27rw+U9mtKgeuXDawRO1B18vXBLyDpyc3P5+9iFLN68F4Cpq3ay3Vsr0Jhg4SSo+4FuIjIZuAbXzXeyiPwZt4JES+BfxR+iMaak1KsWz8CujQB4Y8rqPHfk/WXFTsYv3gbAyMFdePiiTkcNTz+vU336t68LwIPjlrAn/ejRge9MW8tYLxFG+SA3F75aEDqZGRPOShLTcatINAb+gxsk8S/ciL7KwDBVnVgSQRpjSs71fVsAsGrHfibq9qPOH8rO4aEvFwNuwdoLuzQIWY/P5+OhizqREBfNzn0ZPPbdsiPOz1iTwqNfLwVgQJcGDDupCQBf2AK2Jg/hDDOvpao/4LZkT8btUHsFbgHZZqo6tmRCNMaUpPYNqtG3TW0AXp+y+qjz701fx4rt+4jywQMDO+Dz5b2VfKMalfnL2QLARzPWM2ON29dq656D3PLBbLJycmlXP5EnhnQ53HKbvyGVtTv3F/fLMuVAOF18c0Xkn94SR3NU9X+qOlpVf1XVrBKL0BhT4m7o2xKAX1ensHDjnsPHd+7L4JkJywG4vEdTOjasHvL6QNf0an54LcG/f7aQtIOH+NP7s9m5L5Nq8TG8elV3EuJi6NEiifrV3AK4X1oryoQQToKqg9vJ1hhTzvRtU5t29ROBI1tR/xmvpB3MonrlWO7yWkYFiY7yMfKSzkRH+Vi5fR/nPz+FeRtS8fngucu70axWlcPlBnjdhV/M32yL15qjhJOgPgBuFJHmJRSLMSZCfD4f13utqK8XbmFT6gEWbExljLeg7F1ntyWpSlyh6+vYsDrX93H3tjakHADgzv5tOV3qHlHuohNcN9/K7ftYuiUNYwKFs1hsDtAOWCEiK4HtQPDEiVxVPbO4gjPGHD8Duzbkie+WsT0tg7d+WcPc9bvJzYV29ROLtKL67f3b8s2iLWxIOcDZHepx6+mtjyrTqVE1WtSuwpqd+/li/iZbuNYcIZwW1FnATmAjblJuU6BFiC9jTBkUFxPF8N7NAXh76hrmrE8F4P4LOxAT5k6+AJXjonnv2pN55KKOPHdZN6Kijh5c4fP5GNi1IQBfzd+S5zB3UzEVugWlqnkmHxFpAFyFmx9ljCmjruzRjBd+Wkm6t+PuBZ0b0KtV7SLX17x2FZrXrpJvmYEnNOS5H1ewKfUAs9fv5qTmSUV+vkDb0w4yWXdwYdeGxMdGF0ud5vgKez8oPxGJBS4ChgNnA9G4bkBjTBlVPSGWS5ObMGraWuJjo7j3/HYl/pyt6lSlU6NqLNq0l3HzNhdLgtq1L4MhL09nfUo6G3cf4A5vYVxTtoTdbheR7iLyX2ALMAY4H9f1NxJoVbzhGWOOt9v7t+HS5MY8O6wbjWsmHJfnvMibE/X1wi0cyj62z7kHD2Vz/buzWO8tRPv9km3HHJ+JjEK1oESkLq4LbzjQAbeKhL+z+AFgpM2FMqZ8qJEQxxNDuh7X5xzQtQH//nYpKfszmbpyJ/2CRvsVVk5OLnd+PI+53v0zgKVb9rJt70HqeXOuTNmRZwtKRGJE5BIRGYcbGPEkbhWJb4DrgB64RDXfkpMx5lg0qF6ZHl7X3rh5RZ+0+/j4ZXyz0E3XvOe8diRWcp/BJy/fcexBmuMuvxbUZqAWsBcYC3wGfK2q+wBEpFnJh2eMqSgGntCQ39akMH7xVg5kZlM5zg1s2L0/kwlLtzFRt1MpJpoh3RtzSstaR40K/PC39bw62U0yvvqUZtx0akvmrU/lu8Vbmbx8B5cmNznur8kcm/wSVG1gH26C7kTgZ39yMsaY4nZ+pwY88MVi9mdmM3qm20Dx+8XbmLE25Yit5D+bu4kWtatwRY+mDO7emKQqcUxevoN/frEIgDPa1eX+AW7NwNOkDt8t3sqU5TvIys4p0nB5Ezn5JagzcYvBXgHcDOSKyHTgU1xryhhjik3NKnGc2rYOPy3bzkNfLjniXOXYaE5rW4dd+zOYuXY3a3bu51/fLOXJ8crZHesxSXeQnZNLhwbV+O/l3Q4notPa1gFg78Es5m9MpXuz4hnCbo6PPBOUt3XGRBG5FbgAuBI3Yq838BSwHDdQoupxiNMYUwEM7d6Yn5a5LT9qJsTSv309zulYnz5tah+ey6Rb0/jwt3WMnbOJtIysw/tJ1a8Wz1vDT6JKpd/f1hrWqEzbelVZvm0fk3SHJagyxhfOAo0ikggMwSWr0/h97tNE4E3gM1XNb1v4UHVeDtyH2/BwLW5E4Lv5lK8DPAGcg1vRYhpwh6quCCgTgxtdOBx3H202cJeqzggntoD6UhMTE6vPmjWrKJcbY8IwUbdTOTaa5GY18+2SS8/M4sv5m/lwxgZS0zN5+cruIZdK+tfXS3h9yhq6NK7OuNv6lGToJkBycjJpaWl7VLVGUesIK0EFEpH6wOW4LsDuuNZUqqrWCqOOobi5VM8B3wEXA38ChqrqJyHK+4ApuNGEfwV2AQ8B9YHOqrrbK/ciLjn9DVgH3OnFeIKqHr3hTcFxWoIypoyaunInV77xGwCz7utP7aqVIhxRxVAcCarIK0mo6lbgGeAZEWkN/AGXsMIxEvhYVe/wvh8vIknAI8BRCQpog+tivMbfyhKRpcAqYCDwjrfa+k3Abar6ilfme1yX5N24+2nGmAoiuXlNKsdGc+BQNlNW7GBQt8aRDskUUrEMaVHVlar6oKoWbsMYQERa4lae+DTo1CdAOxEJtfaff6Zd4Lr8Kd6jv+V2Bq7r8XC9XrfjV7h7aMaYCqRSTDS9Wrm3h8lq86HKkkiOufQv8qVBx1d6j0clO1VdgLvfdb+ItPPuRz2PGw7/eUC9u1WP+k1cCTQVkcrFEbwxpuzoJ240388rdtqK6WVIJBOUf+/ovUHH/a2jvDaGuRmoCSzF7Ul1Ke6elf/eUvUQdQbWm1ikaI0xZdZpbd3SSSn7M1m4aU8BpU1pEckE5Z8GHvxxxn/8qBUjRaQ98CuwAxiEG8n3JfCpiPQNuD7UR6Q86zXGlG9NayXQ0tv2Y5J185UZkUxQ/o8xwS2lxKDzgfyDKc5W1c9V9XtcC2oubsCG/7pQrS9/vaFaV8aYcu5Ub9Lu5OXbIxyJKaxIJij/vafgfaBbB50P1AxY4h9ODqCqucAvQMeA65JEpGaIeteoauYxRW2MKZP896HmbUglNb3wbwNZ2TkMf3sGF704ldU7bLW34yliCUpVVwJrcBN/Aw0GVqjq+lCXAZ1CJJ+euEm+AD94j4frFZFKuNUwJhxj2MaYMqpny1pUiokiJxemrNhZ6Ou+XbSVSbqD+RtSufjFqUxdWfhrzbEp8jyoYvIw8LaI7MYNAx+I67K7DA6vGtEK12raCzyNm281XkQeA9KBq3GrWlwGoKrrROQd4HkRqQqswE3UrYlbgcIYUwHFx0Zzcsta/Lx8B5O8reAL481f1hz+996DWVz91gwevqgjV55sGzqUtIgu7auqo3ArR5yDGybeD7haVcd4RS4ApgMneuXX4ibqbgVGAaOBJsBZAdeAm6j7CnAPbqWKGK/MSowxFVa/w/ehdhRquPnsdbuZt8FtfvjssBNo36Aa2Tm5/OOzRTw4bjFZx7j7r8lfkZc6qkhsqSNjyodVO/Zx5lOTAfjq//rQqVH1fMvf+sEcvl64hc6NqjPutt6kZ2YzYvQ8Jix128if1rYO/72iG9XiY0s89rKmOJY6ss1RjDEVRsvaVWiS5ObqF7TL7oaUdL5d5FZKv65PC3w+H1UqxfDaVd256bSWh+u45KVppOy3sVclwRKUMabC8Pl8h/eI+vC39ew9eCjPsu9MW0tOLtSrVonzOzc4fDwqyse957XnySFdiI32sXL7PkZNXZNnPaboLEEZYyqU4b2aUykmik2pB7jvs0WEus2xLyOLMTM3AHD1Kc2Jizn6rXJochNuPNW1pD6etfGIXX9N8bAEZYypUFrXTeS+AR0AGDd/M5/O2XRUmY9nbiAtI4v42CiuPLlpnnUNS3bntu49yM8FdBma8FmCMsZUOH84uSlnd6gHwP1fLGLtzv2Hz2Xn5PL2NNdlN/jExtRIiMuznqa1Eujd2q2UPnpmqKmb5lhYgjLGVDg+n4/HB3ehXrVKpGdm8+fRc8nMckPGf1iyjQ0pBwC4tk+oXX+ONOwk14r6cel2tqcdLLmgKyBLUMaYCqlmlTieGXYCPh8s2LiHp35wq6u9+YvbGOGMdnVpVadqgfWc3aEeNRJiycrJZWyI7kJTdJagjDEVVq9Wtbn5tFYAvDp5NS9PWsXMtW6pz+sK0XoCt0LFoG6NABgzc0PIQRfHIjc393DrrqKxBGWMqdDuOKstXZu4uaSPf7cMgHb1Ew/vwlsYw05qAsCanfuZsSalgNKFk5uby9cLttD7sZ/o8/hPrNu1v+CLyhlLUMaYCi02OornLzuBqpV+X5r0Wm9ibmG1q1+NE7wk5x+efizW7NzP1W/N4NYP57B5z0G2p2Xw4LjFxd46K+0sQRljKrxmtarw6MWdAGhYPZ6BhVxINtBlXivq64Vb2HMg7wnA+Tl4KJunv1fOeebnwyuu+1t3E3UH4xdvK1K9ZZUlKGOMAS7u1ohxt/Vm7C29iY+NDvv6AV0bkhAXTUZWDuPmhT9YYuKy7Zz1zGSe/2klmdk5NKpRmdevTubzW3od3svq4S8Xk56ZFXbdZZUlKGOM8XRpXIP61eOLdG3VSjFc2MW1vEaH0c23Iy2D2z6cwx9HzWRDygFio33cenorJtx5Gmd1qIfP5+OhgR2Ji4li856D/PenirMpgyUoY4wpJsN6uG6+xZv3smjTnnzL5n0pEQMAAA8ZSURBVObm8r9ZG+j/9GS+WuAWpe3VqhbfjjiVu89pR+W431txzWpVOTza8I0pq1m5vWLs7GsJyhhjikm3JjVoW8/NncpvZYn1u9L5w5u/cfcnC9hz4BDVK8fy5JAufHD9ybSuG3ru1c39WtE0KYFD2bnc/0XoNQTLG0tQxhhTTHw+3+GVJb6Yu5kDmdlkZGWzdc9Blmzey9SVO3nhpxWc/exkpq7cBcCALg2YcOdpDE1uku/IwfjYaB4a2BGAaat2MW7+5pJ/QREW6S3fjTGmXBnUrRGPf7uMtIwsuj3yPQcPhZ5kW79aPI9c3ImzvDUBC+P/27v/cKuqOo/j73u5XPkh3IAL8kt4BOxL4IT88CEeJTUbnLQ0UVIfs8ZyZsopzSa1KVInNJKZ5DHRUkyxhvwtlmEqZEAqDQpMauB3AEEFCchQLj+ugNz5Y+0Nh+M+l3sO99y7zz2f1/PcZ3PW/rXO8ri/e+219lqnDu3FhGFH8fSKTdw4dyWfGNqLLk2cLHHfvgZeeetdBnbvTE2n0phgUTUoEZFm1L1zNZ/+aJg/Kjs4VVZA7ZHVfHHcQOZ98+N5BafYtZ8ZRof2lWyue4/p81Ydcvtt9Xu4+9m1nHbzQs6a8Rzjpz3D3c+uZU8JTFevKd+bQFO+i0g+6ur38Myrm+nQvh3dO1eHv07V1HRsT2Vl018AzuX2BauZ9qTTrrKCM/6uD8P7duW4vjUM79uVbp3D6Ov/t6mOe59fx5zlG9i5+/0PHGNwz85M/vQwTrVeH1j3+ts7eGTpeh5ZtoF9DQ386msn0qtLfr0bm2PKdz3iExFpZl06tOfs4/sV7fiXnjSIOcs2sGrzdh7/01s8ntEe1e9DHelxZDUvrT/Qi7Bj+3ZMHNWPc0b2Y87yDdy35A3WbNnBJfe8wCnWk8lnDqNPTQfmvryRh5euP2i4pk7V7VptLEDVoJpANSgRSZt3d+7hoaVv7u/SvmbLdrIn9T2mtjMXf2wg547uT03HA+1OKzduY8pvVvD8mtBRo6qyguqqyoNqWn1qOjBxVD/OHzOAAT065Z0/1aBERMpUTaf2XDp+0P7PO3fvZeXGOla89S5vbt3FiUNqGT+kNvGR4kf6dGX2pWOZt2ITNz6xktff3sne3e9TXVXJ6cN7M2l0f04cUku7ZngceTgUoERE2oBO1VWMHtiN0QO7NWn7iooKJgzvzcnWk7kvbWTv+w2cPrx3qnr4KUCJiJSxI6raMXFU/9bORiJ1MxcRkVRSgBIRkVRSgBIRkVRSgBIRkVRSgBIRkVRSgBIRkVRSN/Om6VpXV8eYMWNaOx8iIiWhrq4OoOvhHEMBqmn2AZV1dXXbWjsjIiIloivh2lkwjcUnIiKppDYoERFJJQUoERFJJQUoERFJJQUoERFJJQUoERFJJQUoERFJJQUoERFJJQUoERFJJQUoERFJJQUoERFJJQUoERFJJQ0WK0VjZkcCNwHnAkcCi4Ar3H3VIfabD5yWsOoEd3+x2TOaYmZ2ITAZGASsA6a6+88b2b6gMi8nBZTp54FfJKy6zd2/VpRMCqAalBTXA8Ak4BrgC0A/4PdmVnOI/UYAtwDjsv5WFi+r6WNmk4DZwNPAZ4EFwL1mdl4juxVa5mWhwDIdAazmg7/H/ypqZkU1KCkOMzsJOAP4lLs/GaX9AVgLfIVwl5+0X1+gFnjS3f/YQtlNq6nAg+5+ZfT5KTPrDkwBHs7euNAyLzN5lWlkBLBUv8eWpxqUFMsEoA6YFye4+xZgIeEimsvx0fKl4mUt/cxsEDAYeCRr1cPAUDM7JmG3Qsu8LBRYphACVFn/HluLApQUy1Bgtbu/n5W+GrBG9hsBvAd838z+amb1ZvaEmX24WBlNqaHR0rPSV0fLpDIstMzLRd5lamZ9gF7ASDN71cz2mJmb2cVFzKdE9IhP8mZmVcAFjWyyCagBkmYgrqPxaaBHAEcAu4CJwNHAdcAfzGyEu/+loEyXnrjNKLsM66JlUhkWWublopAyHREtBwFXA/WEtr2fm1mVu9/T7LmU/RSgpBAdSO7VFFsI7AaSpmuuoPFpoG8A7nD338cJZraY0EHi68B3885taaqIltllGKcnlWFFwvZx+mFNvd1GFFKmLwKfARa6exzInjazowjtVgpQRaQAJXlz9+0c+J86kZk9RLjrzNYFeLeRY7+SkPaama3kwN1sOYjLKPuuvkvW+ux98i7zMpJ3mbr7X4HfJBxrLvBJM6uNtpEiUBuUFIsDg8wsO5AN4YNtAACYWYWZXWxm4xNWdwTK6UIQl9GQrPQhWeuz98mrzMtM3mVqZuPM7MsJx+oI7EWBv6gUoKRYngY+BHwyTjCznsDHgflJO7h7A3AVMN3MKjP2G0W4iCwoYn5Txd1XE7qHZ7+fcy6wyt3fSNgt7zIvJwWW6TjgLjP7aJwQ/TbPA55z9z3Fyq/oEZ8UibsvMrMFwP1mdjXwN+B64B3gJ/F2ZjYMOMLdl0dJ1xO6Ac82s7uBAYR2qeU03u7VFn0fuMfMthIeM50FfI6og0oUfAYDK9x9W1PLvMzlVaaENqbLgTlmNpnQoeIy4DhC4JciUg1Kimki8GvCG/ezgPXAae6+NWOb24E58Qd3f5Twhv/gKH1qdIwJCd2n2zR3n0V4wfZ04DHgFOAL7v5AtMmZwGJgVMZuTSnzspVvmUbldjKwBJgOPEgYQuo0d/+flsx7OapoaEjq9CMiItK6VIMSEZFUUoASEZFUUoASEZFUUoASEZFUUoASEZFUUoASEZFU0ou60iaYWRfgn4ELgWMJv+0/A3cBd7l7agZLNbN1wDp3P6WAfXsBO9x9R/R5FvBFd290bMRiiEZUWALc7O6/bGS7WTRjHqMp2K8Axqbpv6s0P9WgpOSZmRFGnZ4KvAx8B7iWMDXCHYSpEVr8At7czOxThPHiemYk3wG01txEXwWqgfta+Ly/JIyF95UWPq+0MNWgpKSZWQfgV4Rp4se4e+bMpz8ys9sIQ9MsAX7cCllsTmMJY+3t5+6LCSMftCgz6wrcCHw1GkOxxbj7PjP7IXCrmf0iYxoMaWNUg5JSdxlhJtQrs4JT7FvAVnS33dwuAdoThgtqDY8SJra8pJXOLy1ANSgpdRcA28nxmMndd5nZWOD1zPRoSo/rgI9FSUuA6919UcY264B5hBu5iwjTfYwEXkhKd/ctZjaOMCBpfNzFwGR3X5LrC0SPH/8F+BLwEcKFfx1hoNJp7t4Qt+NEu6w1s4XufkpS+46ZDSQMsPsPhLmOHJjh7jMztpkV5fFiwrh9JxAGQn0AuMbdd+XKb+Rfgacyt8s45o8JtSsIbYLx+jHRucYSpqm4D/h3d6/PJ+8A7r7TzOZH+Sj1mrHkoBqUlKzowj4SWNrYtAfuvsrdd2fsdxZh6o4BhFlRp0T//l20LtOFwPGERvmZ7r4lV7qZ/T1hNuEa4HuEC+0AYFGOOa5iUwijja8AvkloQ6sHfkiYXhxCW1M8qO6VHAgABzGzYwgB9GxgJmH6kr8Bd5rZtKzNexGm6Hg1+h7PEWYt/o9G8oqZHUvoiDI3YfUAQuC/HrgTyBxQ9ZnoO36DcEPwjeg7FpJ3gMeBD5tZ9vxO0kaoBiWlrJbwG97Y1B3MrAq4DdhAaLPaFqXfAbwC3G5mv80IeB2Bz7n7mqxDHZQe9Wj7KeHCe3I88rqZzQD+l3CXPzIhP+0JQeF+d//HjPS7gM2EuYrudffFZvYScA7wmLuvy/EVpwI9gBPcfVl0rNsI7XTfMrN73f3P0bbdgMvd/dbo80wzW0GoFV6dqwyBk6Jl0iPVjsBl0ajh8XeJ/3mdu0+P0mYSakcTCYEq37xnnn88sLqR/EqJUg1KSlk8/Ua7PPYZBfQnPDbaFie6+zvADKAfMCZj+9UJwSkpfSRhuvXHgG5mVmtmtYQL9uPA8WbWP/sgUSA8itBFPlMtsI0wtUOTmFk7wnQRT8UX+Ogc+wg1rgrC/EeZHsz6/KcoP42Jp5Vfm2P9UznS9z+GjfK0DOh9GHl/LVoec4j8SolSDUpK2VZgN+FRVVPFF7OkKdBXRsuBHOgZtznHcbLTB0fL/4z+khxNmJ8p227gTDM7m9Dh41hC7Qbyu4msJQS0Q323TFuyPr/HoQN+j2i5Lcf6ppbZLkJ7GxSW9/j8tTnOJyVOAUpKVtR5YDEw2syq3H1v0nZmdgMhgFxJuBPPJQ4GuzPSck2SmJ0eX9S/B/wxxz6vJuStAvhvQpvWs8DzhPamRYQ2m3zk+93iGkq+4n0Sg2euiSUPca68856RXlYTWZYTBSgpdY8SZjw9H5idvdLMOgKXEgLI24TecQBDCW0bB20eLd8sIB/xcbe7+/ysPJwAdCfUGLKNJwSnKe5+bcY+VYSaymsJ++SyBdhB+G7ZDue7ZdsULXsQ2vKaQyF5j2tym5A2SW1QUuruJHQh/5GZHZe5ImrX+AmhTeWmqL1nKaFTxWXRy6bxtl0J71RtjLbJ14vRvpeb2f52o+i4DxK6jCfV8OKL7Iqs9H8COnHwTWRcU2is5vJbYIKZ7Z8GPqqlXQM0kNzzLl9xl/2jm+FYQMF5j9v03miufEi6qAYlJc3d683sHEJ36RfMbDahq3IPYBKhK/hDwM3R9nvM7OuEoPFi1FsOQi2rL3BeIY+9so67LDpuPSHQDAQuyvEI8nlCW8p0MxsAvAOcSqgR1hPeBYrF7UVXRT0Nf51wvG8DnwAWmNmthKB5TpR2s7tnB8JCxI8ex5L7cWYh8s17/K7Z75oxD5IiqkFJyXP35YRANAMYR3gZ9LuEC/yXgPMzg467PwJMAN4ivLPzHUKPtFPdveCRETKOu57QFjWFEHzOcvdcLxJvAs4A1kT7/IAQ0C4AbgeGm1ncq+5+YD5h9ISbchxvDSFwPEEYPWMaYXikL7v7vxX63bLOsZ7QJb+xd7sKOW6+eT8JeNndm+sxo6RMRUNDiw6jJSJtgJldQXhvqXdmd/0WPH9X4C/At91dI0m0UapBiUghfkaooU5qpfNPis7/s1Y6v7QABSgRyZu7bycM5XRV1BmlxUTnuwq4IZ4XS9omBSgRKdQthK7hF7XweT8fnfeWFj6vtDC1QYmISCqpBiUiIqmkACUiIqmkACUiIqmkACUiIqmkACUiIqmkACUiIqn0/xB8vlq+lua1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = [(rho, multivariate_normal_auc(d=1, rho=rho))\n",
    "       for rho in np.linspace(-0.9, 0.9)]\n",
    "\n",
    "rhos, aucs = np.transpose(res)\n",
    "plt.plot(rhos, aucs)\n",
    "plt.xlabel('Correlation (rho)')\n",
    "plt.ylabel('Area under ROC')\n",
    "plt.title('AUC as a function of correlation');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### AUC as a function of d\n",
    "\n",
    "The following function contains the code from the previous section, generalized to handle more than 2 dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multivariate_normal_auc(d, num_dims=2):\n",
    "    \"\"\"Generate multivariate normal samples and classify them.\n",
    "    \n",
    "    d: Cohen's effect size along each dimension\n",
    "    num_dims: number of dimensions\n",
    "    \n",
    "    returns: AUC\n",
    "    \"\"\"\n",
    "    # compute the mus\n",
    "    mu1 = np.zeros(num_dims)\n",
    "    mu2 = np.full(num_dims, d)\n",
    "\n",
    "    # and sigma\n",
    "    sigma = np.identity(num_dims)\n",
    "\n",
    "    # generate the samples\n",
    "    sample1 = multivariate_normal(mu1, sigma).rvs(n)\n",
    "    sample2 = multivariate_normal(mu2, sigma).rvs(n)\n",
    "\n",
    "    # label the samples and extract the features and labels\n",
    "    df1 = pd.DataFrame(sample1)\n",
    "    df1['label'] = 1\n",
    "\n",
    "    df2 = pd.DataFrame(sample2)\n",
    "    df2['label'] = 2\n",
    "\n",
    "    df = pd.concat([df1, df2], ignore_index=True)\n",
    "\n",
    "    X = df.drop(columns='label')\n",
    "    y = df.label\n",
    "    \n",
    "    # run the model\n",
    "    model = LogisticRegression(solver='lbfgs').fit(X, y)\n",
    "    y_pred_prob = model.predict_proba(X)[:,1]\n",
    "\n",
    "    # compute AUC\n",
    "    auc = roc_auc_score(y, y_pred_prob)\n",
    "    return auc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Confirming what we have seen before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7680769999999999"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multivariate_normal_auc(d=1, num_dims=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8322470000000001"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multivariate_normal_auc(d=1, num_dims=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now we can sweep a range of effect sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_auc_vs_d(num_dims):\n",
    "    \"\"\"Sweep a range of effect sizes and compute AUC.\n",
    "    \n",
    "    num_dims: number of dimensions\n",
    "    \n",
    "    returns: list of \n",
    "    \"\"\"\n",
    "    effect_sizes = np.linspace(0, 4)\n",
    "\n",
    "    return [(d, multivariate_normal_auc(d, num_dims))\n",
    "            for d in effect_sizes]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "res1 = compute_auc_vs_d(1)\n",
    "res2 = compute_auc_vs_d(2)\n",
    "res3 = compute_auc_vs_d(3)\n",
    "res4 = compute_auc_vs_d(4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "And plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_auc_vs_d(res4, 'num_dim=4')\n",
    "plot_auc_vs_d(res3, 'num_dim=3')\n",
    "plot_auc_vs_d(res2, 'num_dim=2')\n",
    "plot_auc_vs_d(res1, 'num_dim=1')\n",
    "plt.title('AUC vs d for different numbers of features')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With more features, the AUC gets better, assuming the features are independent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
